Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications

In this paper, we propose a new parsimonious transformation for obtaining lifetime distributions, and as special cases, we obtain two new lifetime distributions using exponential and Weibull distributions as baselines in the transformation. We study the mathematical properties of the transformation, and for the two new lifetime distributions, we obtain survival functions, hazard functions, moments, moment-generating functions, mean deviation, Rényi entropy, and quantile function. We estimate the parameters of the new lifetime distributions using the maximum likelihood (ML) estimation method, and the Monte Carlo simulations are used to assess the consistency of the ML estimators of the parameters. The proposed new lifetime distributions provide a better fit in terms of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) scores in comparison to the baseline distributions and other competing models, based on two real datasets, namely the exceedance of the flood peaks of the Wheaton River, and the failure times of 50 items.