On the distribution of the ratio of two hyper-erlang random variables

Therrar Kadri; Khaled Smaili; Seifedine Kadry

doi:10.18576/amis/110121

On the distribution of the ratio of two hyper-erlang random variables

Therrar Kadri
, Khaled Smaili
, Seifedine Kadry

Lebanese International University
Lebanese University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The distribution of ratio of two random variables has been studied by several authors especially when the two random variables are independent and come from the same family. In this paper, the exact distribution of the ratio of two independent Hyper- Erlang distribution is derived. However, closed expressions of the probability density, cumulative distribution function, reliability function, hazard function, moment generating function and the r^th moment are found for this ratio distribution and proved to be a linear combination of the Generalized-F distribution. Moreover, the particular case, the ratio of two independent Hyper-Exponential distribution is examined.

Original language	English
Pages (from-to)	177-182
Number of pages	6
Journal	Applied Mathematics and Information Sciences
Volume	11
Issue number	1
DOIs	https://doi.org/10.18576/amis/110121
State	Published - 2017
Externally published	Yes

Keywords

Erlang distribution
Generalized-F distribution
Hyper-erlang distribution
Log-logistic distribution
Moment generating function
Probability density function
Ratio distribution
Survivor function

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10.18576/amis/110121

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title = "On the distribution of the ratio of two hyper-erlang random variables",

abstract = "The distribution of ratio of two random variables has been studied by several authors especially when the two random variables are independent and come from the same family. In this paper, the exact distribution of the ratio of two independent Hyper- Erlang distribution is derived. However, closed expressions of the probability density, cumulative distribution function, reliability function, hazard function, moment generating function and the rth moment are found for this ratio distribution and proved to be a linear combination of the Generalized-F distribution. Moreover, the particular case, the ratio of two independent Hyper-Exponential distribution is examined.",

keywords = "Erlang distribution, Generalized-F distribution, Hyper-erlang distribution, Log-logistic distribution, Moment generating function, Probability density function, Ratio distribution, Survivor function",

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T1 - On the distribution of the ratio of two hyper-erlang random variables

AU - Kadri, Therrar

AU - Smaili, Khaled

AU - Kadry, Seifedine

PY - 2017

Y1 - 2017

N2 - The distribution of ratio of two random variables has been studied by several authors especially when the two random variables are independent and come from the same family. In this paper, the exact distribution of the ratio of two independent Hyper- Erlang distribution is derived. However, closed expressions of the probability density, cumulative distribution function, reliability function, hazard function, moment generating function and the rth moment are found for this ratio distribution and proved to be a linear combination of the Generalized-F distribution. Moreover, the particular case, the ratio of two independent Hyper-Exponential distribution is examined.

AB - The distribution of ratio of two random variables has been studied by several authors especially when the two random variables are independent and come from the same family. In this paper, the exact distribution of the ratio of two independent Hyper- Erlang distribution is derived. However, closed expressions of the probability density, cumulative distribution function, reliability function, hazard function, moment generating function and the rth moment are found for this ratio distribution and proved to be a linear combination of the Generalized-F distribution. Moreover, the particular case, the ratio of two independent Hyper-Exponential distribution is examined.

KW - Erlang distribution

KW - Generalized-F distribution

KW - Hyper-erlang distribution

KW - Log-logistic distribution

KW - Moment generating function

KW - Probability density function

KW - Ratio distribution

KW - Survivor function

UR - https://www.scopus.com/pages/publications/85010917534

U2 - 10.18576/amis/110121

DO - 10.18576/amis/110121

M3 - Article

AN - SCOPUS:85010917534

SN - 1935-0090

VL - 11

SP - 177

EP - 182

JO - Applied Mathematics and Information Sciences

JF - Applied Mathematics and Information Sciences

IS - 1

ER -

On the distribution of the ratio of two hyper-erlang random variables

Abstract

Keywords

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