Generalizedextended Weibull Power Series Family of Distributions

Abstract

In this study, we introduce a new familyof models for lifetime data called generalized extended Weibullpower series family of distributions by compoundinggeneralizedextended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and nongeneralized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power seriesdistributions proposed by Silva et al. (2013) and the generalized exponential power series distributionsintroduced by Mahmoudi and Jafari (2012).Some mathematical properties of the new class are studied, includingthe cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates.Special subclasses and applications for some models in areal datasetare introduced to demonstrate the flexibility and the benefit of this new family.

Power Lomax Poisson Distribution: Properties and Estimation

“…The probability density, cumulative distribution, reliability and hazard rate functions are obtained. Suppose that = { } =1 be independently and identically distributed (iid) failure times of Z component connected in series and each Y has the power Lomax distribution with pdf (3) and cdf (4). Let the random variable Z has zero-truncated Poisson distribution with probability mass function given by…”

“…which is the cdf of power Lomax distribution as defined in (4). Furthermore, the reliability and hazard rate functions are as follows Figure 1 shows that the density of PLP takes different shapes as symmetrical, right skewed, reversed-J and unimodel.…”