The model identification of beta distribution based on quantiles

E-ISSN： 1563-5163|85|10|2022-2032

ISSN： 0094-9655

Source： Journal of Statistical Computation and Simulation, Vol.85, Iss.10, 2015-07, pp. : 2022-2032

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Abstract

This paper addresses the modelling of a beta distribution based on quantile pairs. The elicited beta distribution is proved to exist uniquely for any given two-quantile pairs. By combining the results of this study with the research documented in the literature, we concluded that for any given two-quantile pairs, there is one and only one beta distribution fits the two specified quantile pairs. The numerical results that verify this finding were obtained by comprehensively examining 1300 two-quantile pairs. The first four moments of the fitted beta distribution were also derived numerically using these two-quantile pairs. The variations in the first four moments, which reflect the perception of uncertainty, were plotted and were explored.