Univariate and Bivariate Log-Topp-Leone Distribution Using Censored and Uncensored Datasets

Abstract

The univariate Topp–Leone distribution introduced by with closed forms of the cumulative distribution function, i.e., [0, 1], was extended to an unbounded limit called the log-Topp–Leone distribution, where the shapes of the hazard function can increase, decrease or remain constant; therefore, this distribution can serve as an alternative distribution to the gamma, Weibull and exponential distributions. The bivariate form of this proposed distribution was introduced by joining the probability density function using three distinct copulas. The MLE, IFM and Bayesian estimation methods were employed to estimate the parameters. The Plackett copula was the best when using the MLE and IFM estimation methods, while the Clayton copula was the best when using the Bayesian method.

Keywords

• log-Topp–Leone distribution
• Farlie–Gumbel–Morgenstern
• Clayton copula
• Plackett copula