A new generalized gamma distribution with applications

SYNOPTIC ABSTRACTThe modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. We introduce and study the gamma-Nadarajah–Haghighi model, which can be interpreted as a truncated generalized gamma distribution (Stacy, 1962 Stacy, E.W. (1962). A generalization of the gamma distribution. Annals of Mathematical Statistics, 33, 1187–1192.[Crossref] , [Google Scholar]). It can have a constant, decreasing, increasing, upside-down bathtub or bathtub-shaped hazard rate function depending on the parameter values. We demonstrate that the new density function can be expressed as a mixture of exponentiated Nadarajah–Haghighi densities. Various of its structural properties are derived, including explicit expressions for the moments, quantile and generating functions, skewness, kurtosis, mean deviations, Bonferroni and Lorenz curves, probability weighted moments, and two types of entropy. We also investigate the order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. We illustrate the flexibility of the new distribution by means of two applications to real datasets.