4. Modelling Survival Data in Medical Research

Statistical Analysis of Reliability Data

Generalizing distributions is an old practice and has ever been considered as precious as many other practical problems in statistics. It simply started with defining different mathematical functional forms, and then induction of location, scale or inequality parameters. The generalization through induction of shape parameter(s) started in 1997, and the last two decades were full of such practices. But to cope with the complex situations under series and parallel structures, the art of mixing discrete and continuous started in 1998. In this article, we present a survey on compounding univariate distributions, their extensions and classes. We review several available compound classes and propose some new ones. The recent trends in the construction of generalized and compounding classes are discussed, and the need for future works are addressed.

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Compounding of distributions: a survey and new generalized classes

DOI: 10.9734/BJMCS/2016/21903 Editor(s): (1) H. M. Srivastava, Department of Mathematics and Statistics, University of Victoria, Canada. Reviewers: (1) G. Y. Sheu, Chang-Jung Christian University, Tainan, Taiwan. (2) P. E. Oguntunde, Covenant University, Nigeria. (3) Thomas L. Toulias, Technological Educational Institute of Athens, Greece. Complete Peer review History: http://sciencedomain.org/review-history/12518

The Complementary Exponentiated Inverted Weibull Power Series Family of Distributions and its Applications

A new lifetime distribution which accommodates decreasing and unimodal hazard function is proposed in this paper. It is derived from the exponentiated complementary exponential geometric distribution and has it genesis on the compounding the exponential and geometric distributions. It can be used on a latent complementary causes scenario, where onle thethe minimum lifetime among all causes is observed. We derive the density, quantile, survival and failure rate functions for the proposed distribution, as well as some proprieties such as the characteristic function, mean, variance and r-th order statistics. The estimation is based on maximum likelihood approach. A simulation study performed in order to assess the performance of the maximum likelihood estimates of the parameters of the proposed distribution. The methodology is illustrated in three real datasets.

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The long-term exponentiated complementary exponential geometric distribution under a latent complementary causes framework

Recently new classes of models have appeared to model survival times, such as, Exponentiated Exponential distribution (Gupta & Kundu, 1999), an extention of Lidley distribution (Bakouch, Al-Zahrani, Al-Shomrani, Marchi, and Louzada, 2011), a generalization of Frechet, gamma, Gumbel (Nadarajah & Kotz, 2006), which can accommodate increasing, decreasing, unimodal hazard functions. In this paper it discussed a generalization of a distribution presented by Louzada, Roman and Cancho (2011), which arise on latent competing risks scenarios, only the maximum lifetime is observed among all risks, that can accommodates increasing hazard functions. The density, survival function and failure rate are presented. Statistical proprieties as characteristic function, moments, r-th order moment, quantile function, residual lifetime distribution are provided. The maximum likelihood estimator and inference from the distribution are discussed. The performance in a real dataset is verified by modeling different distributions to the survival

Cintia Y. Yamachi

Papers

The Exponentiated Complementary Exponential Geometric Distribution

The long-term exponentiated complementary exponential geometric distribution under a latent complementary causes framework