The proportional intermingling of two different exponential distribution terms - Panomram, Waratchaya; Boonthiem, Somchit; Khotama, Supawan; Klongdee, Watcharin (Progress in Applied Science and Technology, 2016)
In this paper we introduce a new distribution, called proportional exponential difference (PED) distribution, such that its probability density function is in the form: <img title="f_{x}\left ( x , α ,λ \right )=\frac{λ }{1-2α }\left ( \left ( 1-α \right )e ^-{\frac{λ x}{1-α }} - α e ^-{\frac{λ x}{α }} \right ),x≥ 0," src="https://latex.codecogs.com/gif.latex?f_{x}\left&space;(&space;x&space;,&space;α&space;,λ&space;\right&space;)=\frac{λ&space;}{1-2α&space;}\left&space;(&space;\left&space;(&space;1-α&space;\right&space;)e&space;^-{\frac{λ&space;x}{1-α&space;}}&space;-&space;α&space;e&space;^-{\frac{λ&space;x}{α&space;}}&space;\right&space;),x≥&space;0,"> where 0" src="https://latex.codecogs.com/gif.latex?λ&space;>&space;0"> และ <img title="α ε \left ( 0,\frac{1}{2} \right )\cup \left ( \frac{1}{2},1 \right )" src="https://latex.codecogs.com/gif.latex?α&space;ε&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 and 1.