# Gamma Distribution

 Probability Home Gamma Distribution

The distribution function of a random variable X distributed according to the gamma distribution with shape parameter ν > 0 is a continuous function, F(x) = P(X < x), given by
F(x) =
 0 for x < 0 [ 1 / Γ(ν) ] ∫0x t (ν - 1)e- t dt for 0 ≤ x

where Γ( ) is the gamma function.

The corresponding probability density function, f(x) = dF(x)/dx, is
f(x) =
 0 for x < 0 [ 1 / Γ(ν) ] x (ν - 1)e- x for 0 ≤ x

#### Function List

• double Gamma_Distribution( double x, double nu )

This function returns F(x) where F(x) is described above.

• double Gamma_Density( double x, double nu )

This function returns f(x) where f(x) is described above.

• void Gamma_Distribution_Tables( double nu, double start, double delta,int nsteps, double *density, double* distribution_function )

This function returns f(x) where f(x) is described above in the array density, i.e. density[i] = f(xi) where xi = start + i delta, i = 0,...,nsteps and returns F(x) where F(x) is described above in the array distribution_function, i.e. distribution_function[i] = F(xi) where xi = start + i delta, i = 0,...,nsteps. Note that density must be declared double density[N] where N ≥ nsteps + 1 in the calling routine and similarly the distribution_function must be declared double distribution_function[N] where
N ≥ nsteps + 1 in the calling routine.

#### Source Code

C source code is available for these routines: