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gampdf

Gamma probability density function

Syntax

Y = gampdf(X,A,B)

Description

Y = gampdf(X,A,B) computes the gamma pdf at each of the values in X using the corresponding shape parameters in A and scale parameters in B. X, A, and B can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. The parameters in A and B must all be positive, and the values in X must lie on the interval [0 ∞).

The gamma pdf is

$y=f\left(x|a,b\right)=\frac{1}{{b}^{a}\Gamma \left(a\right)}{x}^{a-1}{e}^{\frac{-x}{b}}$

The gamma probability density function is useful in reliability models of lifetimes. The gamma distribution is more flexible than the exponential distribution in that the probability of a product surviving an additional period may depend on its current age. The exponential and χ2 functions are special cases of the gamma function.

Examples

The exponential distribution is a special case of the gamma distribution.

mu = 1:5;

y = gampdf(1,1,mu)
y =
0.3679  0.3033  0.2388  0.1947  0.1637

y1 = exppdf(1,mu)
y1 =
0.3679  0.3033  0.2388  0.1947  0.1637