The generalized modified Weibull power series distribution: Theory and applications
提出了一种新的广义修正威布尔幂级数分布，能拟合递增、递减、浴盆形和单峰失效率数据，给出了密度、矩、熵等数学性质及极大似然估计方法，并通过模拟和两个真实数据集展示了其灵活性。
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 r th 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.