scholarly journals Application of a Mixture Cure Fraction Model Based on the Generalized Modified Weibull Distribution for Analyzing Survival of Patients with Breast Cancer

2018 ◽  
Vol 11 (5) ◽  
Author(s):  
Parisa Naseri ◽  
Ahmad Reza Baghestani ◽  
Narges Momenyan ◽  
Mohammad Esmaeil Akbari
Keyword(s):  
Breast Cancer ◽  
Weibull Distribution ◽  
Modified Weibull Distribution ◽  
Model Based ◽  
Cure Fraction ◽  
Generalized Modified Weibull ◽  
Modified Weibull

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.

Improved new modified Weibull distribution: A Bayes study using Hamiltonian Monte Carlo simulation

2020 ◽  
Vol 234 (3) ◽  
pp. 496-511 ◽  
Author(s):  
Tien Thanh Thach ◽  
Radim Bris
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Cross Entropy ◽  
Data Sets ◽  
Hamiltonian Monte Carlo ◽  
Modified Weibull Distribution ◽  
Model Based ◽  
Modified Weibull ◽  
Improved Model ◽  
Better Than

The newly modified Weibull distribution defined in the literature is a model based on combining the Weibull and modified Weibull distributions. It has been demonstrated as the best model for fitting to the bathtub-shaped failure rate data sets. However, another new model based on combining the modified Weibull and Gompertz distributions has been demonstrated later to be even better than the first model. In this article, we have shown how to improve the former model into a better model, and more importantly, we have provided a full Bayesian analysis of the improved model. The Hamiltonian Monte Carlo and cross-entropy methods have been exploited to empower the traditional methods of statistical estimation. Bayes estimators have been obtained using Hamiltonian Monte Carlo for posterior simulations. Bayesian model checking has also been provided in order to check the validation of the model when fitting to real data sets. We have also provided the maximum likelihood estimators of the model parameters using the cross-entropy method to optimize the log-likelihood function. The results derived from the analysis of two well-known data sets show that the improved model is much better than its original form.

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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