In this paper, we first study a new two parameter lifetime distribution. This distribution
includes “monotone” and “non-monotone” hazard rate functions which are useful in lifetime data
analysis and reliability. Some of its mathematical properties including explicit expressions for the
ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and
probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum
likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the
model parameters. The importance and flexibility of the new distribution are illustrated by means of
two applications to real data sets. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit
test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit
test for the Burr X Weibull model