Properties and Applications of the Kumaraswamy Distribution Based on Upper Record Values

Abstract

The Kumaraswamy distribution has attracted the attention of researchers from many fields of application because of its mathematical tractability and its flexibility to accommodate data in various shapes. The distribution is a beta-type distribution, however, the closed-form of its distribution function gives it an advantage over the beta distribution. The aim of this article is to study record values from the Kumaraswamy distribution. The distribution, conditional distribution, moments, mixed moments, and conditional moments of the upper records and, more generally, the  upper records are derived. We also prove some characterizations of the Kumaraswamy distribution based on the upper records. The maximum likelihood, the modified maximum likelihood, and the conditional median predictors of future records are given. A bootstrap procedure is applied to fit the Kumaraswamy distribution to a real dataset: rainfall for the month of January from 1982 to 2021, recorded at the Changi climate station in Singapore, and then future rainfall records are predicted.