The gamma power half-logistic distribution: theory and applications.(English)Zbl 1530.60013
Summary: In this paper, we propose a new three-parameter distribution defined on the positive real line, called the gamma power half-logistic distribution. It constitutes an extension of the power half-logistic distribution using the gamma generated mechanism. The capabilities of the parent distribution are thus improved in several aspects. In particular, the hazard rate function now presents increasing failure, decreasing failure, and bathtub shapes, which are demanded characteristics in the context of statistical modelling. Other features related to the quantiles, skewness, kurtosis, moments, incomplete moments, mean deviations, Bonferroni and Lorenz curves, stochastic ordering, reliability parameter, and distributions of order statistics are also discussed. Subsequently, the gamma power half-logistic model is investigated using real-world results. We use the classical maximum likelihood method for estimating the model parameters, with a simulation trial demonstrating the effectiveness of the method for large enough sample sizes. Then, four real-life data sets of different sizes are used for the concrete application of the model, demonstrating its superiority in fitting compared to similar models.
MSC:
| 60E05 | Probability distributions: general theory |
| 62E15 | Exact distribution theory in statistics |
| 62F10 | Point estimation |
Keywords:
half-logistic distribution;power half-logistic distribution;gamma-G family of distributions;hazard rate;lifetime data;maximum likelihood methodCite
Full Text:DOI
References:
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