Study of the inverse continuous Bernoulli distribution

Abstract

The continuous Bernoulli distribution, a one-parameter probability distribution defined over the interval [0, 1], has recently garnered increased attention in the realm of applied statistics. Numerous studies have underscored both its merits and limitations, alongside proposing extended variants. In this article, we introduce an innovative modification of the continuous Bernoulli distribution through an inverse transformation, thereby introducing the inverse continuous Bernoulli distribution. The main characteristic of this distribution lies in its transposition of the continuous distribution’s properties onto the interval \( [1, +\infty)\), without necessitating any additional parameters. The initial section of this article elucidates the mathematical properties of this novel inverse distribution, encompassing essential probability functions and quantiles. Inference for the associated model is carried out via the widely employed maximum likelihood estimation method. To evaluate the efficacy of the estimated model, a comprehensive simulation study is conducted. Subsequently, the model’s performance is assessed in a practical context, using data sets from a diverse array of sources. Notably, our findings demonstrate its superior performance in comparison to a broad spectrum of analogous models defined over the support interval \( [1, +\infty)\), even surpassing the established Pareto model.