Title: Closed-form mathematical expressions for the exponentiated Cauchy-Rayleigh distribution,
Abstract: The Cauchy-Rayleigh (CR) distribution has been successfully used to describe
asymmetric and heavy-tail events from radar imagery. Employing such model to
describe lifetime data may then seem attractive, but some drawbacks arise: its
probability density function does not cover non-modal behavior as well as the
CR hazard rate function (hrf) assumes only one form. To outperform this
difficulty, we introduce an extended CR model, called exponentiated
Cauchy-Rayleigh (ECR) distribution. This model has two parameters and hrf with
decreasing, decreasing-increasing-decreasing and upside-down bathtub forms. In
this paper, several closed-form mathematical expressions for the ECR model are
proposed: median, mode, probability weighted, log-, incomplete and order
statistic moments and Fisher information matrix. We propose three estimation
procedures for the ECR parameters: maximum likelihood (ML), bias corrected ML
and percentile-based methods. A simulation study is done to assess the
performance of estimators. An application to survival time of heart problem
patients illustrates the usefulness of the ECR model. Results point out that
the ECR distribution may outperform classical lifetime models, such as the
gamma, Birnbaun-Saunders, Weibull and log-normal laws, before heavy-tail data.