Abstract
In this paper, we introduce a new generalized family of distri- butions from bounded support (0,1), namely, the Topp-Leone-G family.Some of mathematical properties of the proposed family have been studied. The new density function can be symmetrical, left-skewed, right-skewed or reverse-J shaped. Furthermore, the hazard rate function can be constant, in- creasing, decreasing, J or bathtub hazard rate shapes. Three special models are discussed. We obtain simple expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations and entropies. The method of maximum likelihood is used to estimate the model parame- ters. The flexibility of the new family is illustrated by means of three real data sets.
Highlights
Several generators have been defined in the literature by introducing one or more parameters to a parent distribution in order to construct more flexible models
(1) We study a new class of distributions based on the TL random variable called the Topp-Leone generalized (TLG) family
If the parent distribution follows the logistic distribution with pdf g(x; λ) = λe−λx(1 + e−λx)−2, x ∈ R and cdf G(x; λ) = (1 + e−λx)−1, the TL logistic (TLLc) pdf is given by fTLLc(x; α, λ) = 2αλe−λx (1 + e−λx)−2 {1 − (1 + e−λx)−1} × [1 − {1 − (1 + e−λx)−1}2]α−1
Summary
Mansoor[1,3], Ayman Alzaatreh, and M. Zubair[1,5]
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