Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Ratio of two independent xgamma random variables and some distributional properties

Subhradev Sen, Suman K. Ghosh, Hazem Al-Mofleh

Abstract

In this investigation, the distribution of the ratio of two independently distributed xgamma (Sen et al. 2016) random variables X and Y , with different parameters, is proposed and studied. The related distributional properties such as, moments, entropy measures, are investigated. We have also shown a unique characterization of the proposed distribution based on truncated incomplete moments.

Ratio of two independent xgamma random variables and some distributional properties

Abstract

In this investigation, the distribution of the ratio of two independently distributed xgamma (Sen et al. 2016) random variables X and Y , with different parameters, is proposed and studied. The related distributional properties such as, moments, entropy measures, are investigated. We have also shown a unique characterization of the proposed distribution based on truncated incomplete moments.
Paper Structure (7 sections, 7 theorems, 26 equations)

This paper contains 7 sections, 7 theorems, 26 equations.

Table of Contents

  1. Introduction
  2. Synthesis of the distribution for $Z=|\frac{X}{Y}|$
  3. Distribution function of the ratio $Z=|\frac{X}{Y}|$
  4. Probability density function of the ratio $Z=|\frac{X}{Y}|$
  5. Moments and related measures
  6. Entropy of $Z=|\frac{X}{Y}|$
  7. Characterization

Key Result

Theorem 1

Suppose that $X$ and $Y$ are independent random variables distributed according to (eqpdf1) and (eqpdf2), respectively. The cumulative density function (cdf) of $Z$ can be expressed as where,

Theorems & Definitions (15)

  • Definition 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • ...and 5 more