New Generalized Rank Mapped Transmuted Exponential Distribution and Some Properties

  • Mohd. Almech Ali Department of Statistics, King Abdulaziz University, Faculty of Science, Jeddah, Saudi Arabia
  • Haseeb Athar Department of Mathematics, College of Science, Taibah University, Al Madinah, Saudi Arabia
  • M.S. Al-Bassam Department of Statistics, King Abdulaziz University, Faculty of Science, Jeddah, Saudi Arabia
Keywords: Transmuted map, order statistics, largest order statistics, exponential distribution, beta distribution, hazard function, family of distributions

Abstract

In this paper, the authors have introduced a new generalized rank mapped transmuted distribution and the proposed distribution has been found to generalize some existing transmuted distributions in literature. The proposed map is applied to the exponential distribution so as to obtain the generalized rank mapped transmuted exponential distribution and its various properties such as nature of the probability curve, mean, variance, skewness, kurtosis with respect to variation in the parameters and the rank of the transmutation map is studied. The hazard rate function and distributional characteristics of the largest order statistics of the generalized rank mapped transmuted exponential distribution is also studied. The generalized rank mapped transmuted exponential distribution is found to model data with higher degree of skewness and kurtosis better than the traditional exponential distribution, which is also one of the utilities of the proposed distribution. If someone is interested to locate more flexible and higher degree of skewed distribution can explore this generalized transmuted distribution for future use.

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Published
2021-09-29
Section
Articles