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Unformatted text preview: Gamma Distribution The gamma distribution with parameters r and can be thought of as the waiting time for r Poisson events when r is integer. The parameter is the expected number of Poisson events per a unit time interval. If increase the typical wait for r events become shorted. (For integer values of r the distribution is also called the Erland distribution). The gamma density is: ¡¢£¤ ¥¦ § ¨ © ª «¢¥§ ¢ £§ ¥¬ ® ¬ £ ¡¯¥©£ ° ± ±©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©¡¯¥©£© ² ³©´ µ The density above is equivalent to the density shown in the text. The above version the density calls attention to the product ¶ x and indicates that 1/ ¶ is a scale factor for x. The standard gamma corresponds to ¶ =1. For the standard gamma E(Y) = ¥ and Var (Y) = ©¥ ´©© The tranformation x = y/ © produce the density above. Hence E(X) = ¥· and Var (X) = ¥· © ¸ ....
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This note was uploaded on 12/20/2011 for the course STAT 344 taught by Professor Staff during the Spring '08 term at George Mason.
- Spring '08