Abstract
A functional composition of the distribution function of one prob ability distribution with the inverse distribution function of another is called the transmutation map. The present paper is purported to show how the transmuted distribution can be obtained by using the convex combination of failure probability of two-component systems. The transmuted Gumbel uni variate exponential distribution is presented by changing convex combination parameter. This new distribution is dened and studied. Some mathematical properties of this distribution including the generating function and ordinary moments are derived. The survival, hazard rate and mean residual life func tions are discussed. Finally, three applications to real data are presented.
Highlights
In the present paper, we will start by examining two-component systems
The transmuted Gumbel univariate exponential distribution is presented by changing convex combination parameter
In the above three tables, it is clear that the values of the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are smaller for the transmuted Gumbel univariate exponential (TGUE) distribution compared to those values of the other models; the new distribution is a very competitive model to these data
Summary
We will start by examining two-component (series and parallel) systems. The transmuted family has been introduced by [27] for the ...rst time and the theory of transmuted distribution is clearly de...ned by [28] This method has led to the development of new and more ‡exible distributions by many authors, proposing many di¤erent distributions and pioneering the modeling of many real data sets with these distributions. Aryal [6] proposed the transmuted loglogistic distribution and discussed various properties of this distribution. Abd El Hady [1] obtained an extended Weibull distribution as the exponentiated transmuted Weibull distribution and discussed its various properties and applications. Elbatal and Aryal [12] studied the transmuted additive Weibull distribution; Merovci [23] proposed the transmuted Rayleigh distribution and discussed their various properties. In order to demonstrate the usefulness of the proposed distribution, three real data applications are presented in the application section
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