# The proportional intermingling of two different exponential distribution terms

## Abstract

In this paper we introduce a new distribution, called proportional exponential difference (PED) distribution, such that its probability density function is in the form:

$f_{x}\left&space;(&space;x&space;,&space;\alpha&space;,\lambda&space;\right&space;)=\frac{\lambda&space;}{1-2\alpha&space;}\left&space;(&space;\left&space;(&space;1-\alpha&space;\right&space;)e&space;^-{\frac{\lambda&space;x}{1-\alpha&space;}}&space;-&space;\alpha&space;e&space;^-{\frac{\lambda&space;x}{\alpha&space;}}&space;\right&space;),x\geq&space;0,$

where $\lambda&space;$ และ $\alpha&space;\epsilon&space;\left&space;(&space;0,\frac{1}{2}&space;\right&space;)\cup&space;\left&space;(&space;\frac{1}{2},1&space;\right&space;)$ . We study some properties of PED distribution such as expected value, variance,  moment generating function and its limit at $\alpha&space;=0,\frac{1}{2}$ and 1.

## Article Details

How to Cite
1.
Panomram W, Boonthiem S, Khotama S, Klongdee W. The proportional intermingling of two different exponential distribution terms. Prog Appl Sci Tech. [Internet]. 2016 Jun. 29 [cited 2024 Aug. 13];6(1):164-9. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/243166
Section
Mathematics and Applied Statistics

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