تحلیل داده های سانسور شده با استفاده از مدل آمیخته فرآیند دیریکله با هسته وارون وایبل تعمیم یافته

در این مقاله یک مدل آمیخته فرایند دیریکله جدید با هسته وارون وایبل تعمیم‌یافته پیشنهاد شده است. پس از تعیین توزیع پیشین پارامترها در مدل پیشنهادی، برای نمونه‌گیری از توزیع پسین توام پارامترها از روش‌های مونت کارلوی زنجیره مارکف استفاده شده است. عملکرد مدل پیشنهادی با تحلیل چندین مجموعه داده واقعی و شبیه‌سازی شده مورد بررسی قرار گرفته است. در مجموعه داده‌های واقعی برخی از داده‌ها سانسور شده از راست هستند. همچنین در این مقاله پتانسیل مدل پیشنهادی برای خوشه‌بندی کردن داده‌ها بکار گرفته شده است. نتایج بدست آمده نشان دهنده عملکرد مطلوب مدل پیشنهادی است.

analysis of censored data using dirichlet process mixture model with generalized inverse weibull distribution as kernel

￿evaluating complex data distribution, such as multimodal cases, requires more complex statistical models. the complexity of a statistical model is related to the number of model parameters. to achieve a more complex model and consequently achieve better flexibility in statistical inference, one can use an infinite-dimensional family of probability models. using the bayesianapproach for the infinite-dimensional parameter need a suitable prior distribution.typically, the prior distribution of such parameters are stochasticprocesses. such priors are called nonparametric bayes priors. the most importantnonparametric bayes prior is the dirichlet process, first introducedby ferguson (1973). due to the discreteness of the dirichlet process, using amixed model of dirichlet processes (dpmm) (antoniak, 1974) is preferable.the ability to cover multimodal data distribution and perform data clusteringare two advantages of dpmms. in this article, we profit from thesetwo advantages of dpmms. kernel selection is an essential issue in workingwith dpmms. according to under study data, a flexible distribution shouldbe selected as the kernel of dpmm. for lifetime data, distributions suchas weibull, lognormal, or other lifetime distributions can be chosen. thegeneralized inverse weibel distribution is a flexible distribution introducedby de gusmão, et al. (2011). in this article, the generalized inverse weibeldistribution is considered the kernel of dpmm.material and methodsin fitting a dpmm, prolongation of the execution time of markov chain monte carlo simulation algorithms is challenging. dirichletprocess packagein r software is a resolution. the mentioned package has a high ability to fitdpmms and other non-parametric bayes models. after obtaining posteriorsamples, survival density and hazard rate functions can be easily estimatedusing this package. finally, by analyzing several real and simulated datasets, the performance of the proposed model is evaluated.results and discussionwe designed a simulation study to evaluate the performance of the proposedmodel under different prior distributions for the accuracy parameter of thedirichlet process based on sample sizes of 100 and 1000. bayesian and intervalestimations of the survival, density, and hazard rate functions of a mixedmodel of two generalized inverse weibull distributions reported. the resultsshow that the proposed model has a high potential in estimating the mentionedfunctions. the proposed model was also used to analyze several realmultimodal data sets. the results show that the proposed model performedbetter compared to other methods. the proposed model is also applied forreal data clustering and simulation.conclusiona mixed model of dirichlet processes with a generalized inverse weibull kernelis used to analyze right-censored survival data. the performance of theproposed model is evaluated based on several simulated and real data sets.achieved results in this paper show that the proposed model has good potentialfor estimating density, survival, and hazard rate functions in survivaldata. another advantage of the proposed model is its high potential for dataclustering..