Gamma(L,*b**,** a*)

Crystal Ball parameter r= estrictions

The Gamma (L,*b**=
,** a*) distribution is right-skewed=
and bounded at L. It is a parametric distribution based on Poisson mathema=
tics. Examples of the Gamma distribution are given below:

The Gamma distribution is extremely important in risk analysis modeling,= with a number of different uses:

The Gamma(0,* b*,

The Gamma distribution is used for its convenience as a description of r=
andom variability of *l* in a Poisson process. It is co=
nvenient because of the identity:

Poisson(Gamma(0,*b*,<=
span>*a*)) =3D NegBinomial(1/(*b*+1),*a*)-*a*

The Gamma distribution can take a variety of shapes, from an Exponential to a Normal, so random variations in *l* for a Poisson can often be well approximated by some Ga=
mma, in which case the Negative Binomial distribut=
ion becomes a neat combination of the two.

In Bayesian inference, the Gamma(0,* b*,

If X is Gamma(0,*b*,* a=
*) distributed, then Y=3DX^(-1/2) is an Inverted Gamma dist=
ribution (InvGamma(0,

The Gamma distribution has also found use in meteorolog= y, inventory theory, insurance risk, economics and queuing theory.

The *Erlang* distribution is the G=
amma distribution for integer values of * a,* i=
.e. Erlang(

The Exponential distribution is a special case of the G=
amma and Erlang: Gamma*(0*,* b=
,1)* =3DErlang

*A Gamma(0,b,*) distribution is the sum of

The Excel function GAMMADIST(x,*a,b*,**0**) returns the probability density function for the Gamm=
a(0,*b,**a*) distribution,=
while GAMMADIST(x,*a,b*,1) returns its cu=
mulative distribution function.