A new inverted Pham distribution for data modeling of mechanical components and diamond in South-West Africa

Abstract This work proposes a new statistical distribution that can fit real-world data more accurately than many other existing models. The new distribution, which has one scale and one shape parameter, is called an inverted Pham distribution. It can model data with upside-down bathtub or decreasing hazard rate shapes. Order statistics and moments are two of the primary characteristics of the inverted Pham distributions that are examined. Eight classical estimation methods are considered to estimate the model parameters. To investigate the accuracy of the various estimation methodologies, a simulation study is conducted. Based on the criteria of mean square error, mean absolute bias, and mean relative error, the numerical results demonstrated that the maximum likelihood estimates, followed by the maximum product of spacing estimates, outperformed other classical estimation methods. By looking at two actual data sets, one based on failure times of mechanical components and the other consisting of diamond size distribution in South-West Africa, the appropriateness of the inverted Pham model and how it compares with some competitive models are demonstrated. The results of two applications based on some goodness of fit criteria, including Akaike information, Anderson-Darling, Cramér-von Mises, and Kolmogorov–Smirnov statistics, showed that the inverted Pham distribution outperformed commonly used distributions like inverted Lomax, inverted Chen, inverted Weibull, inverted gamma, inverted Nadarajah-Haghighi, inverted exponentiated Pareto, generalized inverted exponential, exponentiated inverted exponential, and generalized inverted half-logistic when analyzing real data sets.