GDUS-Modified Topp-Leone Distribution: A New Distribution with Increasing, Decreasing, and Bathtub Hazard Functions

In this paper, we propose an extension to the Topp-Leone distribution, as introduced by [20] using the Generalized-DUS transformation given by [8]. The Topp-Leone distribution is defined on interval (0,1) and has a characteristic J-shaped frequency curve. The newly extended version of Topp-Leone distribution accommodates a variety of shapes of hazard rate functions making it a versatile distribution. We have also derived explicit expressions for some properties like ordinary moments, conditional moments, distribution of order statistics, quantiles, mean deviation, and entropy. Further, we have also discussed results on identifiability, stress-strength reliability, and stochastic ordering that are concerned with two independent random variables. For inference regarding the unknown parameters of the distribution, we derive the equations which give their maximum likelihood estimators. We also present the asymptotic confidence intervals of the unknown parameters of the distribution, based on large sample property, using the Fisher information matrix. To facilitate further studies, a step-by-step algorithm is presented to produce a random sample from the distribution. Further, extensive simulation experiments are done to study the long-term behavior of the maximum likelihood estimators of the parameters through their mean squared error and mean absolute bias on the basis of large number of samples. The consistency of the MLEs is empirically proved. Lastly, the application of the proposed distribution is shown by fitting a real-life dataset over some existing distributions in the same range.