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Unformatted text preview: Special Gamma Distributions There are two special distributions in the family of gamma distributions. They are the exponential distribution and the chi-square distribution. 1. Exponential distribution An exponential distribution is a gamma distribution with α = 1. The only parameter for an exponential distribution is the scale parameter β . Exponential distributions are often used to model the length of life of electronic components. The probability density function of an exponential distribution is f ( y ) = 1 β e- y/β ≤ y < ∞ The distribution function for the exponential distribution has a closed form solution. The distribution function is F ( y ) = P ( Y ≤ y ) = braceleftBigg y < 1- e- y/β ≤ y < ∞ Here are graphs of the probability density function and distribution function of the exponential distribution with β = 1. p.d.f. of Exponential Distribution with mean = 1 y f(y) 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Distribution of Exponential Distribution with mean = 1 y F(y)...
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This note was uploaded on 01/27/2010 for the course STAT 342 taught by Professor Staff during the Spring '08 term at Iowa State.
- Spring '08