A new three-parameter ageing distribution

We propose a new three-parameter ageing distribution called the Weibull–Poisson (WP) distribution, which generalizes the exponential-Poisson (EP) distribution introduced by Kus (2007). This new distribution has a more general form of failure rate (hazard rate) function. With appropriate choice of parameter values, it is able to model three ageing classes of life distributions including decreasing failure rate (DFR), increasing failure rate (IFR), and modified upside-down-bathtub (MUBT)-shaped failure rate. It thus provides an alternative to many existing life distributions. Various properties of this distribution are discussed and the estimation of the parameters is considered by the expectation maximization (EM) algorithm. Also, the asymptotic variance–covariance matrices of these estimates are obtained. Furthermore, some expressions for the Rènyi and Shannon entropies are given. Simulation studies are performed and experimental results are illustrated based on a real data set.