On discriminating between Libby-Novick generalized beta and Kumaraswamy distributions: theory and methods

Abstract

In fitting a continuous bounded data, the generalized beta (and several variants of this distribution) and the two-parameter Kumaraswamy (KW) distributions are the two most prominent univariate continuous distributions that come to our mind. There are some common features between these two rival probability models and to select one of them in a practical situation can be of great interest. Consequently, in this paper, wediscussvariousmethodsofselectionbetweenthegeneralizedbetaproposedbyLibbyandNovick(1982) (LNGB)andtheKWdistributions,suchasthecriteriabasedonprobabilityofcorrectselectionwhichisanimprovementoverthelikelihoodratiostatisticapproach,andalsobasedonpseudo-distancemeasures.We obtain an approximation for the probability of correct selection under the hypotheses H LNGB and H KW , and selectthemodelthatmaximizesit.However,ourproposalismoreappealinginthesensethatweprovidethe comparisonstudyfortheLNGBdistributionthatsubsumesbothtypesofclassicalbetaandexponentiatedgenerators(see,fordetails,Cordeiroetal.2014;LibbyandNovick1982)whichcanbeanaturalcompetitor ofatwo-parameterKWdistributioninanappropriatescenario.