Modified Topp-Leone Distribution: Properties, Classical and Bayesian Estimation with Application to COVID-19 and Reliability Data
Keywords:
Least squares estimation, lifetime data, maximum likelihood estimation, maximum product of spacings, Topp-Leone distributionAbstract
In this article, we have proposed a new continuous model called Modified Topp-Leone distribution. One of the main features of this model is that it has only one parameter but contains varieties of shapes for density and hazard rate functions. We have discussed its various impressive properties like heavy-tailed behavior, mode, moments, quantile, median, skewness, kurtosis, moment generating
function, mean deviation, various inequality measures, mean residual life, expected inactivity time function, weighted moments, entropies, and various other important reliability characteristics including stress-strength reliability, hazard rate, survival function, stochastic ordering, and order statistics. The parameter estimation of the proposed model is discussed in the classical and Bayesian paradigm. In classical point estimation, we have used the method of maximum likelihood, ordinary and weighted least squares, Cramer-Von-Mises, and the method of maximum product of spacings. The asymptotic distribution of the maximum likelihood estimator is also provided and it is used to develop the asymptotic confidence interval. In Bayesian estimation, we have used informative and non-informative priors under symmetric and asymmetric loss functions to obtain the Bayes estimator of the unknown
parameter. The highest posterior density interval of the parameter is also obtained. An extensive simulation study is presented to the assessment of the different estimation procedures. In the end, three real datasets are examined to show the utility of the proposed model in the real world.
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