Expected value of the Gamma distribution with shape parameter \(\alpha\) and rate parameter \(\beta\).

E_gamma(shape, rate = 1/scale, scale = 1/rate)

Arguments

shape

shape parameter \(\alpha\), must be positive integer.

rate

\(\beta\) is the rate parameter, must be positive.

scale

alternative parameterization to rate parameter, scale = 1 / rate.

Value

Function :

Invalid parameter values will return an error detailing which parameter is problematic.

Details

The Gamma distribution with shape parameter \(\alpha\) and rate parameter \(\beta\) has density: $$f\left(x\right) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1}% \textrm{e}^{-\beta x}$$ for \(x \in \mathcal{R}^+\), \(\beta, \alpha > 0\).

See also

Examples

# With scale parameter E_gamma(shape = 3, scale = 4)
#> [1] 12
# With rate parameter E_gamma(shape = 3, rate = 0.25)
#> [1] 12