A new reduced quantile function for generating families of distributions

Abstract

In this paper, a variant of the T-X(Y) generator was developed by suppressing the scale parameter of the classical Lomax distribution in the quantile function. Uniquely, the reduction of the number of parameters essentially accounts for the parsimony of the attendant model. The study considered the Exponential distribution as the transformer and consequently obtained the New Reduced Quantile Exponential-G (NRQE-G) family. The Type-II Gumbel distribution was deployed as the baseline to obtain a special sub-model known as the New Reduced Quantile Exponential Type-II Gumbel (NRQE-T2G) model. Some functional properties of the distribution namely, moment and its related measures such as the mean, variance, second, third, and fourth moments were obtained. The Mode, skewness, Kurtosis, index of dispersion, coefficient of variation, order statistics, survival, hazard, and quantile function were also derived. The maximum likelihood estimation method was used to estimate its parameters. The model's credibility, applicability, and flexibility were proven using two real-life datasets.