Abstract
In this paper, a new method is proposed to expand the family of lifetime distributions. The suggested method is named as Khalil new generalized family (KNGF) of distributions. A special submodel, termed as Khalil new generalized Pareto (KNGP) distribution, is investigated from the family with one shape and two scale parameters. A number of mathematical properties of the submodel have been derived including moments, moment-generating function, quantile function, entropy measures, order statistics, mean residual life function, and maximum likelihood method for the estimation of parameters. The proposed distribution is very flexible in its nature covering several hazard rate shapes (symmetric and asymmetric). To examine the performance of the maximum likelihood estimates in terms of their bias and mean squared error using simulated samples, a simulation study is carried out. Furthermore, parametric estimation of the model is conferred using the method of maximum likelihood, and the practicality of the proposed family is illustrated with the help of real datasets. Finally, we hope that the new suggested flexible KNGF may produce useful models for fitting monotonic and nonmonotonic data related to survival analysis and reliability analysis.