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Why belong exponential family for poisson distribution
Dhuttor Baal
Exponential distribution is a function of probability theory and statistics. This kind of distribution deals with continuous probability distributions and is part of the continuous analogue of the geometric distribution in math.
The geometric distribution is: Pr(X=k) = (1-p)k-1p for k = 1, 2 , 3 ... A geometric series is a+ ar+ ar2, ... or ar+ ar2, ... Now the sum of all probability values of k = Pr(X=1) + Pr(X = 2) + Pr(X = 3) ... = p + p2+p3 ... is a geometric series with a = 1 and the value 1 subtracted from the series. See related links.
This is the only discrete distribution that is memoryless. (In the continuous case the exponential is memoryless.) It's the only one to have this property because it is the only one to count independent trials.