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.

Tropically Adapted Passive Building: A Descriptive-Analytical Approach Using Multiple Linear Regression and Probability Models to Predict Indoor Temperature

“…Meanwhile, another study in India found that the normal distribution gives the best fit, followed by Log-normal and Gamma distributions to model the annual maximum temperature [24]. In a separate study conducted in Nigeria, it was determined that for modeling the groundwater pollutant concentrations, the odd beta prime Fréchet distribution provided the most accurate fit [77].…”

“…A similar study was conducted to evaluate the chemical parameters of groundwater using six probability distributions, such as normal, log-normal, gamma, Weibull, logistic, and log-logistic distributions [33]. The following studies can be referred to for more probability distribution modeling works [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”

Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution

“…These observations further support the novelty and significance of the proposed model. Recent literature has introduced several univariate distributions, such as those in [30][31][32], which often possess complex structures that can complicate their practical use. In contrast, the B-SIOR-G model, described in Equation ( 2), maintains a relatively simple structure.…”

Transformed Log-Burr III Distribution: Structural Features and Application to Milk Production

“…The extension of well-known distributions for modeling real data via generalized classes of distributions has received considerable attention during the last decade. In particular, the recent distributions proposed using the T-X approach include the exponentiated odd Lindley-X family by [7], the Maxwell-Weibull distribution by [8], the Maxwell-Lomax distribution by [9], the Maxwell-exponential distribution by [10], the odd beta prime-G family by [11], the odd beta prime-logistic distribution by [12], the odd beta prime-Fréchet distribution by [13], the log-Topp-Leone distribution by [14], and more others.…”