The New Topp-Leone-Exponential Generator of Distributions with Applications
DOI:
https://doi.org/10.1285/i20705948v19n1p1-34Keywords:
Topp-Leone-G, Generalized Distribution, Estimation Techniques.Abstract
This study introduces a new family of distributions, the Topp–Leone–Exponential generator of distributions. We derive its statistical properties, including the hazard rate function, quantile function, moments, stochastic ordering, order statistics, and R´enyi entropy. For parameter estimation, six parameter estimation methods, namely, maximum likelihood, least-squares, weighted least-squares, Cram´er-von Mises, Anderson–Darling, and Right-Tail Ander-son–Darling are applied, and their consistency is assessed via Monte Carlo simulations for a special case of the new family of distributions. Estimation and application under type I right censoring scheme are presented. Finally, we illustrate the goodness-of-fit of the new family of distributions by fitting a special case to complete and censored data sets from different fields.
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