A Compounded Probability Model for Decreasing Hazard and its Inferential Properties

Early failures are generally observed due to latent defects within a product caused by faulty components, faulty assembly, transportation damage and installation damage. Also early life (infant mortality) failures tend to exhibit a decreasing failure rate over time. Such type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this article a single parameter continuous compounded distribution is proposed to model such type of problems. Some important properties of the proposed distribution such as distribution function, survival function, hazard function and cumulative hazard function, entropies, stochastic ordering are derived. The maximum likelihood estimate of the parameter is obtained which is not in closed form, thus iteration procedure is used to obtain the estimate of parameter. The moments of the proposed distribution does not exist. Some real data sets are used to see the performance of proposed distribution with comparison of some other competent distributions of decreasing hazard using Likelihood, AIC, AICc, BIC and KS statistics.