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Less Restrictive Assumption for Distributional Characterization: A g-and-k Distribution Approach

Azmeri Khan, Sunzida Rahman, Syed Shahadat Hossain

Abstract



Whenever we choose to assume a specific distribution to be fitted to a given set of data, a wrong choice is always a possibility. The consequences of a incorrect assumption will lead to misleading inferences. Consideration of a less restrictive assumption by employing a more general and broader family of distribution may be thought to be one way for avoiding such consequences. In this paper, employment of a g-and-k distribution for the purpose is investigated. To check the adequacy of the use of g-and-k distribution as a underlying assumption on data, a simulation study has been conducted. Data are generated from six different theoretical continuous distributions: normal, logistic, laplace, half-normal, gamma and lognormal. For the generated datasets, both likelihood and Bayesian methods are used to characterize the distribution under both the assumptions that the data comes from the given parent distribution as well as from a g-and-k distribution. For comparison purpose the fitted quantiles of the data under the g-and-k distribution assumption against those under the specific parent distribution assumption are plotted. In the Bayesian set up, the twenty fifth, fiftieth and seventy fifth quantiles generated from the posterior distribution of the parameters using both approaches are compared. In all comparisons, the distribution
characterization under g-and-k distribution assumption performed almost similar to that under the true parent distribution assumption. Fitting real data employing the g-and-k distribution assumption is, that is why, deemed to be as good as fitting without having any rigid assumption, and as a result, is a robust approach in distribution characterization.

Keywords


g-and-k distribution, maximum likelihood method, posterior distribution, MCMC

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