The Inverse Weibull Geometric Distribution: Properties and Estimation

Recently, many statisticians investigate a new family of probability distributions with more flexible in modeling various types of lifetime distributions in practice. They consider a compounded distribution of the well-known lifetime distributions such as exponential, generalized exponential and Weibull random variables with a discrete distribution such as binomial, geometric and truncated Poisson random variables. In this point, we propose the compounded distribution of the inverse Weibull (IW) random variable with a geometric random variable, so-called the inverse Weibull geometric (IWG) distribution. And we study some of its properties including order statistics, moments and moment generating function. Here, the maximum likelihood estimates (MLEs) of the parameters of the proposed distribution are obtained using expectation maximization (EM) algorithm. Also, we compare the proposed distribution with the competing survival models by using Akaike information criterion (AIC) or Bayesian information criterion (BIC). Finally, IWG distribution is applied to the simulated data.