A new two-parameter half-logistic distribution with numerical analysis and applications

The Half-Logistic (HL) distribution is a renowned lifetime distribution widely used in various domains, including reliability engineering, biological sciences, and actuarial research. Despite its fundamental simplicity and easy interpretation, the HL distribution has limitations in terms of flexibility for modeling datasets with heavy tails or varying skewness. To address these constraints, this paper introduces a new extension of the HL distribution based on the Odd Beta Prime (OBP) family. The newly developed distribution has two shape parameters and is named the Odd Beta Prime Half-Logistic (OBPHL) distribution. Its several distributional properties, including the probability density function, cumulative distribution function, survival function, hazard function, and quantile function, alongside other various distributional characteristics, such as moments, measures of skewness and kurtosis, entropy measure ( Rényi and Tsallis), and order statistics, are explored. The maximum likelihood estimation technique is used to estimate the parameters of the new model. The performance of the estimators under different sample sizes has been evaluated using a Monte Carlo simulation study. In addition, the proposed OBPHL distribution is applied to two real-world datasets. The results are compared against several classical distributions using standard model selection criteria. The OBPHL distribution consistently outperforms the competing models based on evaluation metrics. This research contributes a new flexible model to the field of statistical distribution theory and demonstrates its efficacy in practical applications.