Asian Journal of Probability and Statistics

This study introduces a new family of continuous probability distributions, termed the Ishita-G family, using the Transformed-Transformer (T-X) method. The Ishita-G family is generated by combining the Ishita distribution with a baseline distribution through a generator approach, thereby producing more flexible models with varied density and hazard-rate shapes. Three special submodels of the family are defined: the Ishita-Exponential, Ishita-Weibull, and Ishita-Pareto distributions. The study investigates important statistical properties of the Ishita-Exponential distribution (IshExD), including the probability density function, cumulative distribution function, survival function, hazard-rate function, and moment-generating function. The validity of the proposed density function is also established mathematically. The parameters of the IshExD are estimated using maximum likelihood estimation, and a Monte Carlo simulation study is conducted to examine the consistency and efficiency of the estimators. The simulation results show that the estimators perform well as the sample size increases, with decreasing biases and mean squared errors. Furthermore, the usefulness of the proposed family, through the IshExD, is demonstrated using a real-life dataset comprising failure times for repairable items. Model-comparison measures, including the Akaike information criterion (AIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC), and Kolmogorov-Smirnov statistic, show that the Ishita-Exponential distribution outperforms the competing models considered. The results indicate that the Ishita-G family is a flexible and useful contribution to the literature on generalised probability distributions.