A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data

Abstract

In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of probability distributions (FPDs) called the odd beta prime generalized (OBP-G) FPDs is proposed to improve the traditional PDs. A new PD called the odd beta prime-logistic (OBP-logistic) distribution has been developed based on the developed OBP-G FPDs. Some desirable mathematical properties of the proposed OBP-logistic distribution, including the moments, moment-generating function, information-generating function, quantile function, stress–strength, order statistics, and entropies, are studied and derived. The proposed OBP-logistic distribution’s parameters are determined by adopting the maximum likelihood estimation (MLE) method. The applicability of the new PD was demonstrated by employing three data sets and these were compared by the known extended logistic distributions, such as the gamma generalized logistic distribution, new modified exponential logistic distribution, gamma-logistic distribution, exponential modified Weibull logistic distribution, exponentiated Weibull logistic distribution, and transmuted Weibull logistic distribution. The findings reveal that the studied distribution provides better results than the competing PDs. The empirical results showed that the new OBP-logistic distribution performs better than the other PDs based on several statistical metrics. We hoped that the newly constructed OBP-logistic distribution would be an alternative to other well-known extended logistic distributions for the statistical modeling of symmetric and skewed data sets.