Introducing the Half-Logistic Marshall–Olkin XGamma (HLMOXG) Distribution with Enhanced Flexibility

Abstract

Over the past few years, some new probability distributions founded on composite and generalized frameworks have been suggested to offer more flexible statistical models that are able to capture a wide range of data behaviors. Even though the XGamma distribution is effective in the modeling of positively skewed lifetime information, it is not very effective in the analysis of heavy-tailed behavior and intricate pattern of hazard rates.  In order to address these weaknesses, we propose a new distribution, built by the successive use of Half-Logistic generator and the extension with the Marshall-Olkin to XGamma distribution base, which transforms into Half-Logistic-Marshall-Olkin XGamma (HLMOXG) distribution. The proposed model offers the flexibility in shape offered by the MarshallOlkin transformation, even more shape control offered by the HalfLogistic generator, and the desirable characteristics of the XGamma base model.  Statistical properties of the new distribution, such as PDF, CDF, survival and hazard rate functions, and major mathematical properties such as moments, moment-generating function, quantile function and order statistics are calculated and discussed. The estimation of parameters is done using the maximum likelihood estimation (MLE) technique.  To test the performance of the proposed model, a simulation study and real data applications in the fields of reliability and environmental are employed. The relative performance shows that the HLMOXG distribution offers a better goodness-of-fit and more flexibility than the baseline and competing models that prove that the HLMOXG can be an effective instrument to analyze lifetime and reliability data