Gamma.RdGamma distribution with shape parameter \(\alpha\) and rate parameter \(\beta\).
expValGamma(shape, rate = 1/scale, scale = 1/rate) varGamma(shape, rate = 1/scale, scale = 1/rate) kthMomentGamma(k, shape, rate = 1/scale, scale = 1/rate) expValLimGamma(d, shape, rate = 1/scale, scale = 1/rate) expValTruncGamma(d, shape, rate = 1/scale, scale = 1/rate, less.than.d = TRUE) stopLossGamma(d, shape, rate = 1/scale, scale = 1/rate) meanExcessGamma(d, shape, rate = 1/scale, scale = 1/rate) VatRGamma(kap, shape, rate = 1/scale, scale = 1/rate) TVatRGamma(kap, shape, rate = 1/scale, scale = 1/rate) mgfGamma(t, shape, rate = 1/scale, scale = 1/rate)
| shape | shape parameter \(\alpha\), must be positive. |
|---|---|
| rate | rate parameter \(\beta\), must be positive. |
| scale | alternative parameterization to the rate parameter, scale = 1 / rate. |
| k | kth-moment. |
| d | cut-off value. |
| less.than.d | logical; if |
| kap | probability. |
| t | t. |
Function :
expValGamma gives the expected value.
varGamma gives the variance.
kthMomentGamma gives the kth moment.
expValLimGamma gives the limited mean.
expValTruncGamma gives the truncated mean.
stopLossGamma gives the stop-loss.
meanExcessGamma gives the mean excess loss.
VatRGamma gives the Value-at-Risk.
TVatRGamma gives the Tail Value-at-Risk.
mgfGamma gives the moment generating function (MGF).
Invalid parameter values will return an error detailing which parameter is problematic.
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 \(x \in \mathcal{R}^+\), \(\beta, \alpha > 0\).
Function VatRGamma is a wrapper for the qgamma
function stats package.
# With scale parameter expValGamma(shape = 3, scale = 4)#> [1] 12# With rate parameter expValGamma(shape = 3, rate = 0.25)#> [1] 12# With scale parameter varGamma(shape = 3, scale = 4)#> [1] 48# With rate parameter varGamma(shape = 3, rate = 0.25)#> [1] 48# With scale parameter kthMomentGamma(k = 2, shape = 3, scale = 4)#> [1] 192# With rate parameter kthMomentGamma(k = 2, shape = 3, rate = 0.25)#> [1] 192# With scale parameter expValLimGamma(d = 2, shape = 3, scale = 4)#> [1] 1.992244# With rate parameter expValLimGamma(d = 2, shape = 3, rate = 0.25)#> [1] 1.992244# With scale parameter expValTruncGamma(d = 2, shape = 3, scale = 4)#> [1] 0.02101947# With rate parameter expValTruncGamma(d = 2, shape = 3, rate = 0.25)#> [1] 0.02101947# values greather than d expValTruncGamma(d = 2, shape = 3, rate = 0.25, less.than.d = FALSE)#> [1] 11.97898# With scale parameter stopLossGamma(d = 2, shape = 3, scale = 4)#> [1] 10.00776# With rate parameter stopLossGamma(d = 2, shape = 3, rate = 0.25)#> [1] 10.00776# With scale parameter meanExcessGamma(d = 2, shape = 3, scale = 4)#> [1] 74565.87# With rate parameter meanExcessGamma(d = 2, shape = 3, rate = 0.25)#> [1] 74565.87# With scale parameter VatRGamma(kap = .2, shape = 3, scale = 4)#> [1] 6.140177# With rate parameter VatRGamma(kap = .2, shape = 3, rate = 0.25)#> [1] 6.140177# With scale parameter TVatRGamma(kap = .2, shape = 3, scale = 4)#> [1] 13.94824# With rate parameter TVatRGamma(kap = .2, shape = 3, rate = 0.25)#> [1] 13.94824mgfGamma(t = 1, shape = 3, rate = 5)#> [1] 1.953125