scholarly journals Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data

2013 ◽  
Vol 112 (3) ◽  
pp. 343-355 ◽  
Author(s):  
Edson Z. Martinez ◽  
Jorge A. Achcar ◽  
Alexandre A.A. Jácome ◽  
José S. Santos
Keyword(s):  
Gastric Cancer ◽  
Weibull Distribution ◽  
Cancer Data ◽  
Modified Weibull Distribution ◽  
Cure Fraction ◽  
Generalized Modified Weibull ◽  
Modified Weibull ◽  
Fraction Models

Bayesian mixture cure rate frailty models with an application to gastric cancer data

2020 ◽  
pp. 096228022097469
Author(s):  
Ali Karamoozian ◽  
Mohammad Reza Baneshi ◽  
Abbas Bahrampour
Keyword(s):  
Gastric Cancer ◽  
Bayesian Inference ◽  
Weibull Distribution ◽  
Survival Data ◽  
Random Variable ◽  
Frailty Models ◽  
Accurate Estimation ◽  
Cure Rate ◽  
Generalized Modified Weibull ◽  
Modified Weibull

Mixture cure rate models are commonly used to analyze lifetime data with long-term survivors. On the other hand, frailty models also lead to accurate estimation of coefficients by controlling the heterogeneity in survival data. Gamma frailty models are the most common models of frailty. Usually, the gamma distribution is used in the frailty random variable models. However, for survival data which are suitable for populations with a cure rate, it may be better to use a discrete distribution for the frailty random variable than a continuous distribution. Therefore, we proposed two models in this study. In the first model, continuous gamma as the distribution is used, and in the second model, discrete hyper-Poisson distribution is applied for the frailty random variable. Also, Bayesian inference with Weibull distribution and generalized modified Weibull distribution as the baseline distribution were used in the two proposed models, respectively. In this study, we used data of patients with gastric cancer to show the application of these models in real data analysis. The parameters and regression coefficients were estimated using the Metropolis with Gibbs sampling algorithm, so that this algorithm is one of the crucial techniques in Markov chain Monte Carlo simulation. A simulation study was also used to evaluate the performance of the Bayesian estimates to confirm the proposed models. Based on the results of the Bayesian inference, it was found that the model with generalized modified Weibull and hyper-Poisson distributions is a suitable model in practical study and also this model fits better than the model with Weibull and Gamma distributions.

scholarly journals The transmuted generalized modified Weibull distribution

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1395-1412 ◽  
Author(s):  
Gaussm Cordeiro ◽  
Abdus Saboor ◽  
Muhammad Khan ◽  
Serge Provost
Keyword(s):  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Real Data ◽  
Rate Function ◽  
Modified Weibull Distribution ◽  
Positive Data ◽  
Anderson Darling ◽  
Generalized Modified Weibull ◽  
Modified Weibull ◽  
Von Mises

Canada EM [email protected] AU Ortega Edwinm M. AF Universidade de S?o Paulo, Departamento de Ci?ncias Exatas, Piracicaba, Brazil EM [email protected] KW Generalized modifiedWeibull distribution % Goodness-of-fit statistic % Lifetime data % Transmuted family % Weibull distribution KR nema A profusion of new classes of distributions has recently proven useful to applied statisticians working in various areas of scientific investigation. Generalizing existing distributions by adding shape parameters leads to more flexible models. We define a new lifetime model called the transmuted generalized modified Weibull distribution from the family proposed by Aryal and Tsokos [1], which has a bathtub shaped hazard rate function. Some structural properties of the new model are investigated. The parameters of this distribution are estimated using the maximum likelihood approach. The proposed model turns out to be quite flexible for analyzing positive data. In fact, it can provide better fits than related distributions as measured by the Anderson-Darling (A*) and Cram?r-von Mises (W*) statistics, which is illustrated by applying it to two real data sets. It may serve as a viable alternative to other distributions for modeling positive data arising in several fields of science such as hydrology, biostatistics, meteorology and engineering.

A generalized modified Weibull distribution for lifetime modeling

2008 ◽  
Vol 53 (2) ◽  
pp. 450-462 ◽  
Author(s):  
Jalmar M.F. Carrasco ◽  
Edwin M.M. Ortega ◽  
Gauss M. Cordeiro
Keyword(s):  
Weibull Distribution ◽  
Modified Weibull Distribution ◽  
Generalized Modified Weibull ◽  
Modified Weibull
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