The gamma function is part of the formula defining the student's t-distribution:
y = Gamma * ((n+1/2)/Gamma * (n/2)*SQR(n*pi)) * (1+(t^2/n))exp -(n+1)/2 if that makes sense (sorry, I only have ascii on this machine). n = df Since df is a function of sample size (or sizes), the shape of the curve changes as a function of df. Mike On Sun, 16 Feb 2003, Herman Rubin wrote: > In article <[EMAIL PROTECTED]>, > Dana Netherton <[EMAIL PROTECTED]> wrote: > >On Sat, 15 Feb 2003 01:27:34 GMT, [EMAIL PROTECTED] (john v > >verkuilen) said ... > >> Dana Netherton <[EMAIL PROTECTED]> writes: > > >> >So now my question is -- what's a "CDF Gamma" function > >> >anyway? How is it different from "a Gamma function"? > > The rest of what is quoted is below. I believe it will > be clear why. > > Many distributions are named for the functions used to obtain > or describe their probabilities or densities. For example, > the geometric distribution has its probabilities forming a > geometric series. The binomial distribution has the terms > of a binomial expansion, as does the multinomial. The > hypergeometric distribution has terms proportional to the > coefficients in the expansion of a hypergeometric function. > > The exponential distribution has an exponential function > for its density. The double exponential distribution as > exponentials going both ways from the center. The Beta and > Gamma distributions have as their densities the functions > which when integrated give the Beta and Gamma functions. > > >> The Gamma function is an integral which generalizes the factorial since > >> Gamma(x) = (x-1)! for whole numbers x > 1. It is typically defined over > >> non-integer values of x, at least for the purposes of probability theory. > >> You might want to see http://www.math2.org/math/integrals/more/gammafun.htm. > > >> The CDF Gamma is the CDF of the gamma distribution, which is based on the > >> gamma function. It should be discussed in any decent probability theory > >> book. The Gamma distribution is a commonly used waiting-time distribution. > >> I recall there's a connection between it and the Weibull but I can't remember > >> the details and don't have a reference handy. > > >Hmm ... so the gamma distribution function is so-called > >because it uses the gamma function inside it? (Yes, I > >remember seeing the gamma function inside its defining > >formula) > -- > This address is for information only. I do not claim that these views > are those of the Statistics Department or of Purdue University. > Herman Rubin, Deptartment of Statistics, Purdue University > [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
