The generalized modified Weibull power series distribution: Theory and applications
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- 作者：S.F. Bagheri ; E. Bahrami Samani ; ehsan_bahrami_samani@yahoo.com" class="auth_mail" title="E-mail the corresponding author ; M. Ganjali
- 关键词：Generalized modified Weibull distribution ; Power series distributions ; Goodness-of-fit tests ; Hazard function ; EM-algorithm ; Fisher&rsquo ; s information matrix ; Residual life function
- 刊名：Computational Statistics & Data Analysis
- 出版年：2016
- 出版时间：February 2016
- 年：2016
- 卷：94
- 期：Complete
- 页码：136-160
- 全文大小：1070 K
文摘
A new distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate forms called as the generalized modified Weibull power series (GMWPS) distribution is proposed. The new distribution is constructed based on a latent complementary risk problem and is obtained by compounding generalized modified Weibull (GMW) and power series distributions. The new distribution contains, as special submodels, several important distributions which are discussed in the literature, such as generalized modified Weibull Poisson (GMWP) distribution, generalized modified Weibull Geometric (GMWG) distribution, generalized modified Weibull Logarithmic (GMWL) distribution, generalized modified Weibull Binomial (GMWB) distribution, among others.
A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival function, failure rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formula for the elements of the Fisher information matrix. We consider the EM-algorithm for computing the estimates. Simulation studies and two real data set applications are also given for illustration of the flexibility and potentiality of the new distribution.