English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Nowadays, beta and Kumaraswamy distributions are the most popular models tofit continuous bounded data. These models present some characteristics incommon and to select one of them in a practical situation can be of greatinterest. With this in mind, in this paper we propose a method of selectionbetween the beta and Kumaraswamy distributions. We use the logarithm of thelikelihood ratio statistic (denoted by $T_n$, where $n$ is the sample size) andobtain its asymptotic distribution under the hypotheses $H_{\mathcal B}$ and$H_{\mathcal K}$, where $H_{\mathcal B}$ ($H_{\mathcal K}$) denotes that thedata come from the beta (Kumaraswamy) distribution. Since both models has thesame number of parameters, based on the Akaike criterion, we choose the modelthat has the greater log-likelihood value. We here propose to use theprobability of correct selection (given by $P(T_n>0)$ or $P(T_n<0)$ dependingon the null hypothesis) instead of only to observe the maximized log-likelihoodvalues. We obtain an approximation for the probability of correct selectionunder the hypotheses $H_{\mathcal B}$ and $H_{\mathcal K}$ and select the modelthat maximizes it. A simulation study is presented in order to evaluate theaccuracy of the approximated probabilities of correct selection. We illustrateour method of selection in two applications to real data sets involvingproportions.

Beta and Kumaraswamy distributions as non-nested hypotheses in the modeling of continuous bounded data