# Documentation

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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```