Abstract
In this paper, A new class of distributions called the Zografos-Balakrishnan odd log-logistic Generalized half-normal (ZOLL-GHN) family with four parameters is introduced and studied. Useful representations and some mathematical properties of the new family include moments, quantile function, moment Generating function are investigated. The maximum likelihood equations for estimating the parameters based on real data are given. Different methods have been used to estimate its parameters such as maximum likelihood, Least squares, weighted least squares, Crammer-von-Misers,Anderson-Darling and right-tailed Anderson-Darling methods. We assesses the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family and fitness capability of this model, are illustrated by means of two real data sets.
Highlights
The statistics literature is filled with hundreds of continuous univariate distributions: see Johnson et al [19, 20]
Cordiro et al [10] introduced a new family of distribution which called Zografos-Balakrishnan odd log-logisticG
Equation (25) reveals that the qt of the ZBOLL-GHN distribution can be expressed as a power series
Summary
The statistics literature is filled with hundreds of continuous univariate distributions: see Johnson et al [19, 20]. Cordiro et al [10] introduced a new family of distribution which called Zografos-Balakrishnan odd log-logisticG. 212 THE ZOGRAFOS-BALAKRISHNAN ODD LOG-LOGISTIC GENERALIZED HALF-NORMAL DISTRIBUTION. Gleaton and Lynch [16] introduced a new family of distribution which called generalized log-logistic G. 2. Zografos-Balakrishnan odd log-logistic generalized half-normal (ZOLL-GHN) distribution. The Generalized Half Normal(GHN) distribution is introduced by Cooray and Ananda [6] This density function with shape parameter λ > 0 and scale parameter θ > 0 (for x > 0), where τ = (λ, θ)T , (Cooray and Ananda, [6]). By using (8) and (9) in equations (3) and (2), the density function and cd of ZOLL-GHN(for x > 0), with four parameters λ > 0, θ > 0, α > 0 and β > 0, are given by the following:.
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