Logarithmic Transformed Topp-Leone Family of Distributions: Properties, and Applications
Keywords:
Logarithmic transformation, logarithmic transformed Topp-Leone family of distributions, probability weighted moments, maximum likelihood estimationAbstract
This study introduces a novel family of continuous distributions called the logarithmic transformed Topp-Leone family. Key statistical properties of the proposed family are investigated, including the hazard rate, reverse hazard rate, odds function, moments, moment-generating function, residual and reverse residual life moments, entropy measures, order statistics, probability-weighted moments, and quantile function. Parameter estimation is performed using both maximum likelihood and maximum product spacing methods. To demonstrate the flexibility of the proposed family, the Lindley distribution is considered the baseline distribution, and the logarithmic transformed Topp-Leone Lindley distribution is derived, for which comprehensive statistical properties are also derived. The performance of the proposed estimators is evaluated through comprehensive Monte Carlo simulations.
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