Beta generated slash distribution: derivation, properties and application to lifetime data

Year 2024, Volume: 73 Issue: 3, 641 - 663, 27.09.2024

Sahana Bhattacharjee , Nandita Borah

https://doi.org/10.31801/cfsuasmas.1398868

Abstract

In this paper, we introduce a new distribution called beta generated slash distribution by applying the slash construction idea to the existing beta distribution of first kind. The statistical properties of the distribution such as moments, skewness, kurtosis, median, moment generating function, mean deviations, Lorenz and Bonferroni curves, order statistics, Mills ratio, hazard rate functions have been discussed. The location-scale form of the beta generated slash distribution is also established. The hazard rate function is seen to assume different shapes depending upon the values of the parameters. The method of maximum likelihood is used to estimate the unknown parameters of beta generated slash distribution and a simulation study is conducted to check the performance of these estimates. Finally, the proposed distribution is applied to a real-life data set on failure times and the goodness-of-fit of the fitted distribution is compared with four other competing distributions to show its flexibility and advantage particularly in modeling heavy tailed data sets.

Keywords

Beta distribution, slash construction approach, Lorenz and Bonferroni curves, estimation, simulation

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