xid-7781382_1

xid-7781382_1 - Gamma Distribution The gamma distribution...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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) = ¥· © ¸ ....
View Full Document

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.

Page1 / 5

xid-7781382_1 - Gamma Distribution The gamma distribution...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online