Abstract
Within the master thesis [1], the author considered the following random variable $$T=X^{-1}-1,$$ where $X$ follows the Kumaraswamy distribution, and obtains a so-called inverted Kumaraswamy distribution, and studies some properties and applications of this class of distributions in the context of the power series family [2]. Within the paper [3], they introduced the exponentiated generalized class of distributions and obtained some properties with applications. Based on these developments we introduce a class of modified power series inverted exponentiated generalized distributions and obtain some of their properties with applications. Some characterization theorems are also presented. Avenues for further research concludes the paper.
Highlights
The exponentiated class of distributions first appeared in [4], with the following representation for its CDFReceived: July 1, 2020; Accepted: July 23, 20202010 Mathematics Subject Classification: 62Exx, 62E10.Keywords and phrases: exponentiated generalized, power series, characterization theorems, carbon fibers data.Copyright c 2021 the AuthorF (x)β, where F (x) is some baseline distribution and β > 0
(1 − (1 − F (x))α)β, It is well known that the inverse distribution is the distribution of the reciprocal of a random variable
Based on the stochastic representation X(1) = min{X1, · · ·, XN ) we study some properties and applications of a certain modified power series inverted Exponentiated Generalized distribution
Summary
The exponentiated class of distributions first appeared in [4], with the following representation for its CDF. The power series class of distributions was proposed and studied in [2] This class of distributions includes binomial, geometric, logarithmic and Poisson distributions as special cases. These distributions may not be useful when a random variable takes the value of zero with high probability, that is, zero-inflated. Suppose X follows the Exponentiated Standard Uniform Generalized Distribution, and consider the transformation discussed earlier. Based on the stochastic representation X(1) = min{X1, · · · , XN ) we study some properties and applications of a certain modified power series inverted Exponentiated Generalized distribution (by relaxing the domain space of y∗- see new family defined )
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