The Weibull-Power Cauchy distribution: model, properties and applications

Abstract

We propose a new three-parameter distribution with increasing, decreasing, reversed-J and upside-down bathtub shaped hazard rate, called the Weibull-power Cauchy distribution. We obtain explicit expressions for the mode, ordinary, negative and incomplete moments, mean deviations, mean residual life, quantile and generating functions, order statistics, Shannon entropy and reliability. We derive a power series
for the quantile function using exponential partial Bell polynomials. A useful characterization of the new distribution is also presented. The
method of maximum likelihood is used to estimate the model parameters. The importance of the new distribution is proved empirically by
means of three real-life data sets.

Keywords

• Cauchy distribution,half-Cauchy distribution,moments,power Cauchy distribution,T-X family,Weibull-X family

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