xid-7781382_1

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

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

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: 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) = . When r= 1, the gamma distribution is the exponential distribution. The mean of exponential distribution is 1/ and the variance is The gamma cumulative distribution in R is given by pgamma(q, shape, rate) where q (q for qauntile) is the upper bound on the left tail of the distribution, shape is the same as r and rate is the same as . Graphics further below show the distribution shape changes as r increases.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern