, Samuel Mwalili [aut,
ctb], Oscar Ngesa [aut, ctb], Christophe Chesneau [aut, ctb]| Title: | Tractable Parametric Odds-Based Regression Models |
|---|---|
| Description: | Fits tractable fully parametric odds-based regression models for survival data, including proportional odds (PO), accelerated failure time (AFT), accelerated odds (AO), and General Odds (GO) models in overall survival frameworks. Given at least an R function specifying the survivor, hazard rate and cumulative distribution functions, any user-defined parametric distribution can be fitted. We applied and evaluated a minimum of seventeen (17) various baseline distributions that can handle different failure rate shapes for each of the four different proposed odds-based regression models. For more information see Bennet et al., (1983) <doi:10.1002/sim.4780020223>, and Muse et al., (2022) <doi:10.1016/j.aej.2022.01.033>. |
| Authors: | Abdisalam Hassan Muse [aut, cre]
, Samuel Mwalili [aut,
ctb], Oscar Ngesa [aut, ctb], Christophe Chesneau [aut, ctb] |
| Maintainer: | Abdisalam Hassan Muse <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2024-11-21 05:36:26 UTC |
| Source: | https://github.com/cran/AmoudSurv |
The alloauto data frame has 101 rows and 3 columns.
This data frame contains the following columns:
time: Time to death or relapse, months
type :Type of transplant (1=allogeneic, 2=autologous)
delta:Leukemia-free survival indicator (0=alive without relapse, 1=dead or relapse)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa,Christophe Chesneau, [email protected]
Klein and Moeschberger (1997) Survival Analysis Techniques for Censored and truncated data, Springer. Kardaun Stat. Nederlandica 37 (1983), 103-126.
{ data(alloauto) str(alloauto) }{ data(alloauto) str(alloauto) }
Bone marrow transplant study which is widely used in the hazard-based regression models
There were 46 patients in the allogeneic treatment and 44 patients in the autologous treatment group
Time: time to event
Status: censor indicator, 0 for censored and 1 for uncensored
TRT: 1 for autologous treatment group; 0 for allogeneic treatment group
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, [email protected]
Robertson, V. M., Dickson, L. G., Romond, E. H., & Ash, R. C. (1987). Positive antiglobulin tests due to intravenous immunoglobulin in patients who received bone marrow transplant. Transfusion, 27(1), 28-31.
The gastric data frame has 90 rows and variables.It is a data set from a clinical trial conducted by the Gastrointestinal Tumor Study Group (GTSG) in 1982. The data set refers to the survival times of patients with locally nonresectable gastric cancer. Patients were either treated with chemotherapy combined with radiation or chemotherapy alone.
This data frame contains the following columns:
time: survival times in days
trt :treatments (1=chemotherapy + radiation; 0=chemotherapy alone)
status:failure indicator (1=failure, 0=otherwise)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa,Christophe Chesneau, [email protected]
Gastrointestinal Tumor Study Group. (1982) A Comparison of Combination Chemotherapy and Combined Modality Therapy for Locally Advanced Gastric Carcinoma. Cancer 49:1771-7.
{ data(gastric) str(gastric);head(gastric) }{ data(gastric) str(gastric);head(gastric) }
Larynx Cancer-Patients data set which is widely used in the survival regression models
The data frame contains 90 rows and 5 columns:
time: time to event, in months
delta: Censor indicator, 0 alive and 1 for dead
stage: Stage of disease (1=stage 1, 2=stage2, 3=stage 3, 4=stage 4)
diagyr: Year of diagnosis of larynx cancer
age: Age at diagnosis of larynx cancer
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, [email protected]
Klein and Moeschberger (1997) Survival Analysis Techniques for Censored and truncated data, Springer. Kardaun Stat. Nederlandica 37 (1983), 103-126.
Tractable Parametric accelerated failure time (AFT) model's maximum likelihood estimation, log-likelihood, and information criterion. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
MLEAFT( init, times, status, n, basehaz, z, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )MLEAFT( init, times, status, n, basehaz, z, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )
init |
: initial points for optimisation |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic accelerated failure time "NGLLAFT" model, generalized log-logisitic accelerated failure time "GLLAFT" model, modified log-logistic accelerated failure time "MLLAFT" model, exponentiated Weibull accelerated failure time "EWAFT" model, power generalized weibull accelerated failure time "PGWAFT" model, generalized gamma accelerated failure time "GGAFT" model, modified kumaraswamy Weibull proportional odds "MKWAFT" model, log-logistic accelerated failure time "LLAFT" model, tangent-log-logistic accelerated failure time "TLLAFT" model, sine-log-logistic accelerated failure time "SLLAFT" model, cosine log-logistic accelerated failure time "CLLAFT" model, secant-log-logistic accelerated failure time "SCLLAFT" model, arcsine-log-logistic accelerated failure time "ASLLAFT" model, arctangent-log-logistic accelerated failure time "ATLLAFT" model, Weibull accelerated failure time "WAFT" model, gamma accelerated failure time "GAFT", and log-normal accelerated failure time "LNAFT") |
z |
: design matrix for covariates (p x n), p >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEAFT(init = c(1.0,0.20,0.05),times = time,status = delta,n=nrow(z), basehaz = "WAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEAFT(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEAFT(init = c(1.0,0.50,0.5),times = time,status = delta,n=nrow(z), basehaz = "LLAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #4 data("larynx") time<-larynx$time delta<-larynx$delta larynx$age<-as.numeric(scale(larynx$age)) larynx$diagyr<-as.numeric(scale(larynx$diagyr)) larynx$stage<-as.factor(larynx$stage) z<-model.matrix(~ stage+age+diagyr, data = larynx) MLEAFT(init = c(1.0,0.5,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE)#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEAFT(init = c(1.0,0.20,0.05),times = time,status = delta,n=nrow(z), basehaz = "WAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEAFT(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEAFT(init = c(1.0,0.50,0.5),times = time,status = delta,n=nrow(z), basehaz = "LLAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #4 data("larynx") time<-larynx$time delta<-larynx$delta larynx$age<-as.numeric(scale(larynx$age)) larynx$diagyr<-as.numeric(scale(larynx$diagyr)) larynx$stage<-as.factor(larynx$stage) z<-model.matrix(~ stage+age+diagyr, data = larynx) MLEAFT(init = c(1.0,0.5,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "LNAFT",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE)
A Tractable Parametric Accelerated Odds (AO) model's maximum likelihood estimates,log-likelihood, and Information Criterion values. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
MLEAO( init, times, status, n, basehaz, z, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )MLEAO( init, times, status, n, basehaz, z, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )
init |
: Initial parameters to maximize the likelihood function; |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic accelerated odds "NGLLAO" model, generalized log-logisitic accelerated odds "GLLAO" model, modified log-logistic accelerated odds "MLLAO" model,exponentiated Weibull accelerated odds "EWAO" model, power generalized weibull accelerated odds "PGWAO" model, generalized gamma accelerated odds "GGAO" model, modified kumaraswamy Weibull accelerated odds "MKWAO" model, log-logistic accelerated odds "LLAO" model, tangent-log-logistic accelerated odds "TLLAO" model, sine-log-logistic accelerated odds "SLLAO" model, cosine log-logistic accelerated odds "CLLAO" model,secant-log-logistic accelerated odds "SCLLAO" model, arcsine-log-logistic accelerated odds "ASLLAO" model,arctangent-log-logistic accelerated odds "ATLLAO" model, Weibull accelerated odds "WAO" model, gamma accelerated odds "WAO" model, and log-normal accelerated odds "ATLNAO" model.) |
z |
: design matrix for covariates (p x n), p >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEAO(init = c(1.0,0.40,0.50,0.50),times = time,status = delta,n=nrow(z), basehaz = "GLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "CLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "LNAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #4 data("larynx") time<-larynx$time delta<-larynx$delta larynx$age<-as.numeric(scale(larynx$age)) larynx$diagyr<-as.numeric(scale(larynx$diagyr)) larynx$stage<-as.factor(larynx$stage) z<-model.matrix(~ stage+age+diagyr, data = larynx) MLEAO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "ASLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEAO(init = c(1.0,0.40,0.50,0.50),times = time,status = delta,n=nrow(z), basehaz = "GLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "CLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEAO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "LNAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #4 data("larynx") time<-larynx$time delta<-larynx$delta larynx$age<-as.numeric(scale(larynx$age)) larynx$diagyr<-as.numeric(scale(larynx$diagyr)) larynx$stage<-as.factor(larynx$stage) z<-model.matrix(~ stage+age+diagyr, data = larynx) MLEAO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "ASLLAO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
A Tractable Parametric General Odds (GO) model's Log-likelihood, MLE and information criterion values. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
MLEGO( init, times, status, n, basehaz, z, zt, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )MLEGO( init, times, status, n, basehaz, z, zt, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )
init |
: initial points for optimisation |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic general odds "NGLLGO" model, generalized log-logisitic general odds "GLLGO" model, modified log-logistic general odds "MLLGO" model,exponentiated Weibull general odds "EWGO" model, power generalized weibull general odds "PGWGO" model, generalized gamma general odds "GGGO" model, modified kumaraswamy Weibull general odds "MKWGO" model, log-logistic general odds "LLGO" model, tangent-log-logistic general odds "TLLGO" model, sine-log-logistic general odds "SLLGO" model, cosine log-logistic general odds "CLLGO" model,secant-log-logistic general odds "SCLLGO" model, arcsine-log-logistic general odds "ASLLGO" model, arctangent-log-logistic general odds "ATLLGO" model, Weibull general odds "WGO" model, gamma general odds "WGO" model, and log-normal general odds "ATLNGO" model.) |
z |
: design matrix for odds-level effects (p x n), p >= 1 |
zt |
: design matrix for time-dependent effects (q x n), q >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEGO(init = c(1.0,0.50,0.50,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "PGWGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEGO(init = c(1.0,0.50,0.45,0.5),times = time,status = delta,n=nrow(z), basehaz = "TLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEGO(init = c(1.0,1.0,0.50,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "GLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEGO(init = c(1.0,0.50,0.50,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "PGWGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEGO(init = c(1.0,0.50,0.45,0.5),times = time,status = delta,n=nrow(z), basehaz = "TLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEGO(init = c(1.0,1.0,0.50,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "GLLGO",z = z,zt=z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
Tractable Parametric Proportional Odds (PO) model's maximum likelihood estimation, log-likelihood, and information criterion. Baseline hazards: NGLL,GLL,MLL,PGW, GG, EW, MKW, LL, TLL, SLL,CLL,SCLL,ATLL, and ASLL
MLEPO( init, times, status, n, basehaz, z, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )MLEPO( init, times, status, n, basehaz, z, method = "BFGS", hessian = TRUE, conf.int = 0.95, maxit = 1000, log = FALSE )
init |
: initial points for optimisation |
times |
: survival times |
status |
: vital status (1 - dead, 0 - alive) |
n |
: The number of the data set |
basehaz |
: baseline hazard structure including baseline (New generalized log-logistic proportional odds "NGLLPO" model, generalized log-logisitic proportional odds "GLLPO" model, modified log-logistic proportional odds "MLLPO" model, exponentiated Weibull proportional odds "EWPO" model, power generalized weibull proportional odds "PGWPO" model, generalized gamma proportional odds "GGPO" model, modified kumaraswamy Weibull proportional odds "MKWPO" model, log-logistic proportional odds "PO" model, tangent-log-logistic proportional odds "TLLPO" model, sine-log-logistic proportional odds "SLLPO" model, cosine log-logistic proportional odds "CLLPO" model, secant-log-logistic proportional odds "SCLLPO" model, arcsine-log-logistic proportional odds "ASLLPO" model, and arctangent-log-logistic proportional odds "ATLLPO" model, Weibull proportional odds "WPO" model, gamma proportional odds "GPO" model, and log-normal proportional odds "LNPO" model.) |
z |
: design matrix for covariates (p x n), p >= 1 |
method |
:"optim" or a method from "nlminb".The methods supported are: BFGS (default), "L-BFGS", "Nelder-Mead", "SANN", "CG", and "Brent". |
hessian |
:A function to return (as a matrix) the hessian for those methods that can use this information. |
conf.int |
: confidence level |
maxit |
:The maximum number of iterations. Defaults to 1000 |
log |
:log scale (TRUE or FALSE) |
a list containing the output of the optimisation (OPT) and the log-likelihood function (loglik)
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEPO(init = c(1.0,0.40,1.0,0.50),times = time,status = delta,n=nrow(z), basehaz = "GLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEPO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "SLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEPO(init = c(1.0,0.50,1.0,0.75),times = time,status = delta,n=nrow(z), basehaz = "PGWPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #4 data("larynx") time<-larynx$time delta<-larynx$delta larynx$age<-as.numeric(scale(larynx$age)) larynx$diagyr<-as.numeric(scale(larynx$diagyr)) larynx$stage<-as.factor(larynx$stage) z<-model.matrix(~ stage+age+diagyr, data = larynx) MLEPO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "ATLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)#Example #1 data(alloauto) time<-alloauto$time delta<-alloauto$delta z<-alloauto$type MLEPO(init = c(1.0,0.40,1.0,0.50),times = time,status = delta,n=nrow(z), basehaz = "GLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #2 data(bmt) time<-bmt$Time delta<-bmt$Status z<-bmt$TRT MLEPO(init = c(1.0,1.0,0.5),times = time,status = delta,n=nrow(z), basehaz = "SLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE) #Example #3 data("gastric") time<-gastric$time delta<-gastric$status z<-gastric$trt MLEPO(init = c(1.0,0.50,1.0,0.75),times = time,status = delta,n=nrow(z), basehaz = "PGWPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000, log=FALSE) #Example #4 data("larynx") time<-larynx$time delta<-larynx$delta larynx$age<-as.numeric(scale(larynx$age)) larynx$diagyr<-as.numeric(scale(larynx$diagyr)) larynx$stage<-as.factor(larynx$stage) z<-model.matrix(~ stage+age+diagyr, data = larynx) MLEPO(init = c(1.0,1.0,0.5,0.5,0.5,0.5,0.5,0.5),times = time,status = delta,n=nrow(z), basehaz = "ATLLPO",z = z,method = "BFGS",hessian=TRUE, conf.int=0.95,maxit = 1000,log=FALSE)
Arcsine-Log-logistic (ASLL) Cumulative Distribution Function.
pASLL(t, alpha, beta)pASLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the ASLL Cumulative Distribution Function.
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
t=runif(10,min=0,max=1) pASLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) pASLL(t=t, alpha=0.7, beta=0.5)
Arctangent-Log-logistic (ATLL) Cumulative Distribution Function.
pATLL(t, alpha, beta)pATLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the ATLL Cumulative Distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Alkhairy, I., Nagy, M., Muse, A. H., & Hussam, E. (2021). The Arctan-X family of distributions: Properties, simulation, and applications to actuarial sciences. Complexity, 2021.
t=runif(10,min=0,max=1) pATLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) pATLL(t=t, alpha=0.7, beta=0.5)
Cosine-Log-logistic (SLL) Cumulative Distribution Function.
pCLL(t, alpha, beta)pCLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the CLL Cumulative Distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Souza, L., Junior, W. R. D. O., de Brito, C. C. R., Ferreira, T. A., & Soares, L. G. (2019). General properties for the Cos-G class of distributions with applications. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), 63-79.
t=runif(10,min=0,max=1) pCLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) pCLL(t=t, alpha=0.7, beta=0.5)
Generalised Gamma (GG) Probability Density Function.
pdGG(t, kappa, alpha, eta, log = FALSE)pdGG(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the GG probability density function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pdGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)t=runif(10,min=0,max=1) pdGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
Exponentiated Weibull (EW) Cumulative Distribution Function.
pEW(t, lambda, kappa, alpha, log.p = FALSE)pEW(t, lambda, kappa, alpha, log.p = FALSE)
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
the value of the EW cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pEW(t=t, lambda=0.65,kappa=0.45, alpha=0.25, log.p=FALSE)t=runif(10,min=0,max=1) pEW(t=t, lambda=0.65,kappa=0.45, alpha=0.25, log.p=FALSE)
Gamma (G) Cumulative Distribution Function.
pG(t, shape, scale)pG(t, shape, scale)
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
the value of the G Cumulative Distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pG(t=t, shape=0.85, scale=0.5)t=runif(10,min=0,max=1) pG(t=t, shape=0.85, scale=0.5)
Generalised Gamma (GG) Cumulative Distribution Function.
pGG(t, kappa, alpha, eta, log.p = FALSE)pGG(t, kappa, alpha, eta, log.p = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
the value of the GG cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)t=runif(10,min=0,max=1) pGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)
Generalized Log-logistic (GLL) cumulative distribution function.
pGLL(t, kappa, alpha, eta)pGLL(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the GLL cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Muse, A. H., Mwalili, S., Ngesa, O., Almalki, S. J., & Abd-Elmougod, G. A. (2021). Bayesian and classical inference for the generalized log-logistic distribution with applications to survival data. Computational intelligence and neuroscience, 2021.
t=runif(10,min=0,max=1) pGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)t=runif(10,min=0,max=1) pGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)
Log-logistic (LL) Cumulative Distribution Function.
pLL(t, kappa, alpha)pLL(t, kappa, alpha)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
the value of the LL cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pLL(t=t, kappa=0.5, alpha=0.35)t=runif(10,min=0,max=1) pLL(t=t, kappa=0.5, alpha=0.35)
Lognormal (LN) Cumulative Distribution Function.
pLN(t, kappa, alpha)pLN(t, kappa, alpha)
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
the value of the LN cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pLN(t=t, kappa=0.75, alpha=0.95)t=runif(10,min=0,max=1) pLN(t=t, kappa=0.75, alpha=0.95)
Modified Kumaraswamy Weibull (MKW) Cumulative Distribution Function.
pMKW(t, alpha, kappa, eta)pMKW(t, alpha, kappa, eta)
t |
: positive argument |
alpha |
: Inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
the value of the MKW cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)t=runif(10,min=0,max=1) pMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)
Modified Log-logistic (MLL) cumulative distribution function.
pMLL(t, kappa, alpha, eta)pMLL(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the MLL cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Kayid, M. (2022). Applications of Bladder Cancer Data Using a Modified Log-Logistic Model. Applied Bionics and Biomechanics, 2022.
t=runif(10,min=0,max=1) pMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)t=runif(10,min=0,max=1) pMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)
New Generalized Log-logistic (NGLL) cumulative distribution function.
pNGLL(t, kappa, alpha, eta, zeta)pNGLL(t, kappa, alpha, eta, zeta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
the value of the NGLL cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Hassan Muse, A. A new generalized log-logistic distribution with increasing, decreasing, unimodal and bathtub-shaped hazard rates: properties and applications, in Proceedings of the Symmetry 2021 - The 3rd International Conference on Symmetry, 8–13 August 2021, MDPI: Basel, Switzerland, doi:10.3390/Symmetry2021-10765.
t=runif(10,min=0,max=1) pNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)t=runif(10,min=0,max=1) pNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)
Power Generalised Weibull (PGW) cumulative distribution function.
pPGW(t, kappa, alpha, eta)pPGW(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the PGW cumulative distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Alvares, D., & Rubio, F. J. (2021). A tractable Bayesian joint model for longitudinal and survival data. Statistics in Medicine, 40(19), 4213-4229.
t=runif(10,min=0,max=1) pPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)t=runif(10,min=0,max=1) pPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)
Secant-log-logistic (SCLL) Cumulative Distribution Function.
pSCLL(t, alpha, beta)pSCLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the SCLL Cumulative Distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Souza, L., de Oliveira, W. R., de Brito, C. C. R., Chesneau, C., Fernandes, R., & Ferreira, T. A. (2022). Sec-G class of distributions: Properties and applications. Symmetry, 14(2), 299.
t=runif(10,min=0,max=1) pSCLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) pSCLL(t=t, alpha=0.7, beta=0.5)
Sine-Log-logistic (SLL) Cumulative Distribution Function.
pSLL(t, alpha, beta)pSLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the SLL Cumulative Distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Souza, L., Junior, W., De Brito, C., Chesneau, C., Ferreira, T., & Soares, L. (2019). On the Sin-G class of distributions: theory, model and application. Journal of Mathematical Modeling, 7(3), 357-379.
t=runif(10,min=0,max=1) pSLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) pSLL(t=t, alpha=0.7, beta=0.5)
Tangent-Log-logistic (TLL) Cumulative Distribution Function.
pTLL(t, alpha, beta)pTLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the TLL Cumulative Distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pTLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) pTLL(t=t, alpha=0.7, beta=0.5)
Weibull (W) Cumulative Distribution Function.
pW(t, kappa, alpha)pW(t, kappa, alpha)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
the value of the W Cumulative Distribution function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) pW(t=t, kappa=0.75, alpha=0.5)t=runif(10,min=0,max=1) pW(t=t, kappa=0.75, alpha=0.5)
Arcsine-Log-logistic (ASLL) Hazard Rate Function.
rASLL(t, alpha, beta, log = FALSE)rASLL(t, alpha, beta, log = FALSE)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the ASLL Hazard Rate Function.
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)t=runif(10,min=0,max=1) rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Arctangent-Log-logistic (ATLL) Hazard Function.
rATLL(t, alpha, beta, log = FALSE)rATLL(t, alpha, beta, log = FALSE)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the ATLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rATLL(t=t, alpha=0.7, beta=0.5,log=FALSE)t=runif(10,min=0,max=1) rATLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Cosine-Log-logistic (CLL) Hazard Function.
rCLL(t, alpha, beta, log = FALSE)rCLL(t, alpha, beta, log = FALSE)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the CLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Souza, L., Junior, W. R. D. O., de Brito, C. C. R., Ferreira, T. A., & Soares, L. G. (2019). General properties for the Cos-G class of distributions with applications. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), 63-79.
t=runif(10,min=0,max=1) rCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)t=runif(10,min=0,max=1) rCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Exponentiated Weibull (EW) Hazard Function.
rEW(t, lambda, kappa, alpha, log = FALSE)rEW(t, lambda, kappa, alpha, log = FALSE)
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the EW hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Khan, S. A. (2018). Exponentiated Weibull regression for time-to-event data. Lifetime data analysis, 24(2), 328-354.
t=runif(10,min=0,max=1) rEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75, log=FALSE)t=runif(10,min=0,max=1) rEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75, log=FALSE)
Gamma (G) Hazard Function.
rG(t, shape, scale, log = FALSE)rG(t, shape, scale, log = FALSE)
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
log |
:log scale (TRUE or FALSE) |
the value of the G hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rG(t=t, shape=0.5, scale=0.85,log=FALSE)t=runif(10,min=0,max=1) rG(t=t, shape=0.5, scale=0.85,log=FALSE)
Generalised Gamma (GG) Hazard Function.
rGG(t, kappa, alpha, eta, log = FALSE)rGG(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the GG hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Agarwal, S. K., & Kalla, S. L. (1996). A generalized gamma distribution and its application in reliabilty. Communications in Statistics-Theory and Methods, 25(1), 201-210.
t=runif(10,min=0,max=1) rGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)t=runif(10,min=0,max=1) rGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log=FALSE)
Generalized Log-logistic (GLL) hazard function.
rGLL(t, kappa, alpha, eta, log = FALSE)rGLL(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the GLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Muse, A. H., Mwalili, S., Ngesa, O., Alshanbari, H. M., Khosa, S. K., & Hussam, E. (2022). Bayesian and frequentist approach for the generalized log-logistic accelerated failure time model with applications to larynx-cancer patients. Alexandria Engineering Journal, 61(10), 7953-7978.
t=runif(10,min=0,max=1) rGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, log=FALSE)t=runif(10,min=0,max=1) rGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, log=FALSE)
Log-logistic (LL) Hazard Function.
rLL(t, kappa, alpha, log = FALSE)rLL(t, kappa, alpha, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the LL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rLL(t=t, kappa=0.5, alpha=0.35,log=FALSE)t=runif(10,min=0,max=1) rLL(t=t, kappa=0.5, alpha=0.35,log=FALSE)
Lognormal (LN) Hazard Function.
rLN(t, kappa, alpha, log = FALSE)rLN(t, kappa, alpha, log = FALSE)
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
log |
:log scale (TRUE or FALSE) |
the value of the LN hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rLN(t=t, kappa=0.5, alpha=0.75,log=FALSE)t=runif(10,min=0,max=1) rLN(t=t, kappa=0.5, alpha=0.75,log=FALSE)
Modified Kumaraswamy Weibull (MKW) Hazard Function.
rMKW(t, alpha, kappa, eta, log = FALSE)rMKW(t, alpha, kappa, eta, log = FALSE)
t |
: positive argument |
alpha |
: inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the MKW hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Khosa, S. K. (2019). Parametric Proportional Hazard Models with Applications in Survival analysis (Doctoral dissertation, University of Saskatchewan).
t=runif(10,min=0,max=1) rMKW(t=t, alpha=0.35, kappa=0.7, eta=1.4, log=FALSE)t=runif(10,min=0,max=1) rMKW(t=t, alpha=0.35, kappa=0.7, eta=1.4, log=FALSE)
Modified Log-logistic (MLL) hazard function.
rMLL(t, kappa, alpha, eta, log = FALSE)rMLL(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the MLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9,log=FALSE)t=runif(10,min=0,max=1) rMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9,log=FALSE)
New Generalized Log-logistic (NGLL) hazard function.
rNGLL(t, kappa, alpha, eta, zeta, log = FALSE)rNGLL(t, kappa, alpha, eta, zeta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the NGLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4, log=FALSE)t=runif(10,min=0,max=1) rNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4, log=FALSE)
Power Generalised Weibull (PGW) hazard function.
rPGW(t, kappa, alpha, eta, log = FALSE)rPGW(t, kappa, alpha, eta, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the PGW hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6,log=FALSE)t=runif(10,min=0,max=1) rPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6,log=FALSE)
Secant-log-logistic (SCLL) Hazard Function.
rSCLL(t, alpha, beta, log = FALSE)rSCLL(t, alpha, beta, log = FALSE)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the SCLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Souza, L., de Oliveira, W. R., de Brito, C. C. R., Chesneau, C., Fernandes, R., & Ferreira, T. A. (2022). Sec-G class of distributions: Properties and applications. Symmetry, 14(2), 299.
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
t=runif(10,min=0,max=1) rSCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)t=runif(10,min=0,max=1) rSCLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Sine-Log-logistic (SLL) Hazard Function.
rSLL(t, alpha, beta, log = FALSE)rSLL(t, alpha, beta, log = FALSE)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the SLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Souza, L. (2015). New trigonometric classes of probabilistic distributions. esis, Universidade Federal Rural de Pernambuco, Brazil.
t=runif(10,min=0,max=1) rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)t=runif(10,min=0,max=1) rSLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Tangent-Log-logistic (TLL) Hazard Function.
rTLL(t, alpha, beta, log = FALSE)rTLL(t, alpha, beta, log = FALSE)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the TLL hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Muse, A. H., Tolba, A. H., Fayad, E., Abu Ali, O. A., Nagy, M., & Yusuf, M. (2021). Modelling the COVID-19 mortality rate with a new versatile modification of the log-logistic distribution. Computational Intelligence and Neuroscience, 2021.
t=runif(10,min=0,max=1) rTLL(t=t, alpha=0.7, beta=0.5,log=FALSE)t=runif(10,min=0,max=1) rTLL(t=t, alpha=0.7, beta=0.5,log=FALSE)
Weibull (W) Hazard Function.
rW(t, kappa, alpha, log = FALSE)rW(t, kappa, alpha, log = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
log |
:log scale (TRUE or FALSE) |
the value of the w hazard function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) rW(t=t, kappa=0.75, alpha=0.5,log=FALSE)t=runif(10,min=0,max=1) rW(t=t, kappa=0.75, alpha=0.5,log=FALSE)
Arcsine-Log-logistic (ASLL) Survival Function.
sASLL(t, alpha, beta)sASLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the ASLL Survival Function.
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Tung, Y. L., Ahmad, Z., & Mahmoudi, E. (2021). The Arcsine-X Family of Distributions with Applications to Financial Sciences. Comput. Syst. Sci. Eng., 39(3), 351-363.
t=runif(10,min=0,max=1) sASLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) sASLL(t=t, alpha=0.7, beta=0.5)
Arctangent-Log-logistic (ATLL) Survivor Function.
sATLL(t, alpha, beta)sATLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the ATLL Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Alkhairy, I., Nagy, M., Muse, A. H., & Hussam, E. (2021). The Arctan-X family of distributions: Properties, simulation, and applications to actuarial sciences. Complexity, 2021.
t=runif(10,min=0,max=1) sATLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) sATLL(t=t, alpha=0.7, beta=0.5)
Cosine-Log-logistic (CLL) Survivor Function.
sCLL(t, alpha, beta)sCLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the CLL Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Mahmood, Z., M Jawa, T., Sayed-Ahmed, N., Khalil, E. M., Muse, A. H., & Tolba, A. H. (2022). An Extended Cosine Generalized Family of Distributions for Reliability Modeling: Characteristics and Applications with Simulation Study. Mathematical Problems in Engineering, 2022.
t=runif(10,min=0,max=1) sCLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) sCLL(t=t, alpha=0.7, beta=0.5)
Exponentiated Weibull (EW) Survivor Function.
sEW(t, lambda, kappa, alpha)sEW(t, lambda, kappa, alpha)
t |
: positive argument |
lambda |
: scale parameter |
kappa |
: shape parameter |
alpha |
: shape parameter |
the value of the EW survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Rubio, F. J., Remontet, L., Jewell, N. P., & Belot, A. (2019). On a general structure for hazard-based regression models: an application to population-based cancer research. Statistical methods in medical research, 28(8), 2404-2417.
t=runif(10,min=0,max=1) sEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75)t=runif(10,min=0,max=1) sEW(t=t, lambda=0.9, kappa=0.5, alpha=0.75)
Gamma (G) Survivor Function.
sG(t, shape, scale)sG(t, shape, scale)
t |
: positive argument |
shape |
: shape parameter |
scale |
: scale parameter |
the value of the G Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sG(t=t, shape=0.85, scale=0.5)t=runif(10,min=0,max=1) sG(t=t, shape=0.85, scale=0.5)
Generalised Gamma (GG) Survival Function.
sGG(t, kappa, alpha, eta, log.p = FALSE)sGG(t, kappa, alpha, eta, log.p = FALSE)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
log.p |
:log scale (TRUE or FALSE) |
the value of the GG survival function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)t=runif(10,min=0,max=1) sGG(t=t, kappa=0.5, alpha=0.35, eta=0.9,log.p=FALSE)
Generalized Log-logistic (GLL) survivor function.
sGLL(t, kappa, alpha, eta)sGLL(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the GLL survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Muse, A. H., Mwalili, S., Ngesa, O., Alshanbari, H. M., Khosa, S. K., & Hussam, E. (2022). Bayesian and frequentist approach for the generalized log-logistic accelerated failure time model with applications to larynx-cancer patients. Alexandria Engineering Journal, 61(10), 7953-7978.
t=runif(10,min=0,max=1) sGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)t=runif(10,min=0,max=1) sGLL(t=t, kappa=0.5, alpha=0.35, eta=0.9)
Log-logistic (LL) Survivor Function.
sLL(t, kappa, alpha)sLL(t, kappa, alpha)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
the value of the LL survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sLL(t=t, kappa=0.5, alpha=0.35)t=runif(10,min=0,max=1) sLL(t=t, kappa=0.5, alpha=0.35)
Lognormal (LN) Survivor Hazard Function.
sLN(t, kappa, alpha)sLN(t, kappa, alpha)
t |
: positive argument |
kappa |
: meanlog parameter |
alpha |
: sdlog parameter |
the value of the LN Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sLN(t=t, kappa=0.75, alpha=0.95)t=runif(10,min=0,max=1) sLN(t=t, kappa=0.75, alpha=0.95)
Modified Kumaraswamy Weibull (MKW) Survivor Function.
sMKW(t, alpha, kappa, eta)sMKW(t, alpha, kappa, eta)
t |
: positive argument |
alpha |
: Inverse scale parameter |
kappa |
: shape parameter |
eta |
: shape parameter |
the value of the MKW survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)t=runif(10,min=0,max=1) sMKW(t=t,alpha=0.35, kappa=0.7, eta=1.4)
Modified Log-logistic (MLL) survivor function.
sMLL(t, kappa, alpha, eta)sMLL(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the MLL survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Kayid, M. (2022). Applications of Bladder Cancer Data Using a Modified Log-Logistic Model. Applied Bionics and Biomechanics, 2022.
t=runif(10,min=0,max=1) sMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)t=runif(10,min=0,max=1) sMLL(t=t, kappa=0.75, alpha=0.5, eta=0.9)
New Generalized Log-logistic (NGLL) survivor function.
SNGLL(t, kappa, alpha, eta, zeta)SNGLL(t, kappa, alpha, eta, zeta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
zeta |
: shape parameter |
the value of the NGLL survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Hassan Muse, A. A new generalized log-logistic distribution with increasing, decreasing, unimodal and bathtub-shaped hazard rates: properties and applications, in Proceedings of the Symmetry 2021 - The 3rd International Conference on Symmetry, 8–13 August 2021, MDPI: Basel, Switzerland, doi:10.3390/Symmetry2021-10765.
t=runif(10,min=0,max=1) SNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)t=runif(10,min=0,max=1) SNGLL(t=t, kappa=0.5, alpha=0.35, eta=0.7, zeta=1.4)
Power Generalised Weibull (PGW) survivor function.
sPGW(t, kappa, alpha, eta)sPGW(t, kappa, alpha, eta)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
eta |
: shape parameter |
the value of the PGW survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Alvares, D., & Rubio, F. J. (2021). A tractable Bayesian joint model for longitudinal and survival data. Statistics in Medicine, 40(19), 4213-4229.
t=runif(10,min=0,max=1) sPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)t=runif(10,min=0,max=1) sPGW(t=t, kappa=0.5, alpha=1.5, eta=0.6)
Secant-log-logistic (SCLL) Survivor Function.
sSCLL(t, alpha, beta)sSCLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the SCLL Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sSCLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) sSCLL(t=t, alpha=0.7, beta=0.5)
Sine-Log-logistic (SLL) Survivor Function.
sSLL(t, alpha, beta)sSLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the SLL Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
Souza, L., Junior, W., De Brito, C., Chesneau, C., Ferreira, T., & Soares, L. (2019). On the Sin-G class of distributions: theory, model and application. Journal of Mathematical Modeling, 7(3), 357-379.
t=runif(10,min=0,max=1) sSLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) sSLL(t=t, alpha=0.7, beta=0.5)
Tangent-Log-logistic (TLL) Survivor Function.
sTLL(t, alpha, beta)sTLL(t, alpha, beta)
t |
: positive argument |
alpha |
: scale parameter |
beta |
: shape parameter |
the value of the TLL Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sTLL(t=t, alpha=0.7, beta=0.5)t=runif(10,min=0,max=1) sTLL(t=t, alpha=0.7, beta=0.5)
Weibull (W) Survivor Function.
sW(t, kappa, alpha)sW(t, kappa, alpha)
t |
: positive argument |
kappa |
: scale parameter |
alpha |
: shape parameter |
the value of the W Survivor function
Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau [email protected]
t=runif(10,min=0,max=1) sW(t=t, kappa=0.75, alpha=0.5)t=runif(10,min=0,max=1) sW(t=t, kappa=0.75, alpha=0.5)