Transmuted Aradhana Distribution: Properties and Application

Abstract

In this paper, we introduce a new continuous distribution called transmuted Aradhana distribution (TAD). It is a generalization of Aradhana distribution based on the quadratic rank transmutation map. Properties of the proposed distribution including shape of the density, reliability and hazard rate functions, mean residual life function, rth moment, moment generating function, order statistics,
Renyi entropy, quantile function, are explored. We use maximum likelihood method and method of moments to estimate the parameters of the TAD. We present an application to real life data set to illustrate the usefulness of the proposed distribution.
It is shown that the TAD is more adequate for modeling this data than Aradhana distribution and some other available distributions.

Key words and phrases. Transmuted Aradhana distribution, Reliability, Moments, Skewness, Kurtosis, Entropy, Order statistics, Quantile function.

2000 Mathematics Subject Classification. 62H10, 62H12