On a new test of fit to the beta distribution

Abstract

We propose a new L2‐type goodness‐of‐fit test for the family of beta distributions based on a conditional moment characterization. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates that the new procedure outperforms most of the classical tests. Finally, the procedure is applied to a real data set related to air humidity.

Goodness of fit test for uniform distribution with censored observation

“…(Ebner & Liebenberg, 2021 ) Let X be a random variable taking values in [0, 1]. Then for if and only if where I ( A ) denotes the indicator function of a set A .…”

“…Even though several goodness of fit tests have been proposed in the literature for uniform distribution, to the best of our knowledge these tests do not accommodate censored lifetimes. This motivates us to develop new goodness of fit test for uniform distribution for complete data as well as censored data based on a conditional moment characterization [see Ahmed ( 1991 ) and Ebner and Liebenberg ( 2021 )].…”