TL;DR
This paper explores two extensions of a classical problem involving a random variable uniformly distributed between two independent variables, introducing new types of two-sided power distributions for better modeling and analysis.
Contribution
It introduces the concept of two-sided power random variables through two novel extensions, expanding the theoretical framework of power distributions.
Findings
Defined two-sided power random variables.
Developed two extensions: conditionally directed and undirected power distributions.
Provided theoretical properties of the new distributions.
Abstract
We study a well-known problem concerning a random variable uniformly distributed between two independent random variables. Two different extensions, conditionally directed power distribution and conditionally undirected power distribution, have been introduced for this problem. For the second method, two-sided power random variables have been defined.
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Taxonomy
TopicsProbability and Risk Models · Statistical Distribution Estimation and Applications