Exp.RdExponential distribution with rate parameter \(\beta\).
expValExp(rate = 1/scale, scale = 1/rate) varExp(rate = 1/scale, scale = 1/rate) kthMomentExp(k, rate = 1/scale, scale = 1/rate) expValLimExp(d, rate = 1/scale, scale = 1/rate) expValTruncExp(d, rate = 1/scale, scale = 1/rate, less.than.d = TRUE) stopLossExp(d, rate = 1/scale, scale = 1/rate) meanExcessExp(d, rate = 1/scale, scale = 1/rate) VatRExp(kap, rate = 1/scale, scale = 1/rate) TVatRExp(kap, rate = 1/scale, scale = 1/rate) mgfExp(t, rate = 1/scale, scale = 1/rate)
| 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 :
expValExp gives the expected value.
varExp gives the variance.
kthMomentExp gives the kth moment.
expValLimExp gives the limited mean.
expValTruncExp gives the truncated mean.
stopLossExp gives the stop-loss.
meanExcessExp gives the mean excess loss.
VatRExp gives the Value-at-Risk.
TVatRExp gives the Tail Value-at-Risk.
mgfExp gives the moment generating function (MGF).
Invalid parameter values will return an error detailing which parameter is problematic.
The Exponential distribution with rate parameter \(\beta\) has density: $$f\left(x\right) = \frac{1}{\beta}\textrm{e}^{-\beta x}$$ f(x) = b^a e^-b x for \(x \in \mathcal{R}^+\), \(\beta > 0\).
Function VatRExp is a wrapper of the qexp
function from the stats package.
# With scale parameter expValExp(scale = 4)#> [1] 4# With rate parameter expValExp(rate = 0.25)#> [1] 4# With scale parameter varExp(scale = 4)#> [1] 16# With rate parameter varExp(rate = 0.25)#> [1] 16# With scale parameter kthMomentExp(k = 2, scale = 4)#> [1] 32# With rate parameter kthMomentExp(k = 2, rate = 0.25)#> [1] 32# With scale parameter expValLimExp(d = 2, scale = 4)#> [1] 1.573877# With rate parameter expValLimExp(d = 2, rate = 0.25)#> [1] 1.573877# With scale parameter expValTruncExp(d = 2, scale = 4)#> [1] 0.360816# With rate parameter, values greater than d expValTruncExp(d = 2, rate = 0.25, less.than.d = FALSE)#> [1] 3.639184# With scale parameter stopLossExp(d = 2, scale = 4)#> [1] 2.426123# With rate parameter stopLossExp(d = 2, rate = 0.25)#> [1] 2.426123# With scale parameter meanExcessExp(d = 2, scale = 4)#> [1] 4# With rate parameter meanExcessExp(d = 5, rate = 0.25)#> [1] 4# With scale parameter VatRExp(kap = .99, scale = 4)#> [1] 18.42068# With rate parameter VatRExp(kap = .99, rate = 0.25)#> [1] 18.42068# With scale parameter TVatRExp(kap = .99, scale = 4)#> [1] 22.42068# With rate parameter TVatRExp(kap = .99, rate = 0.25)#> [1] 22.42068mgfExp(t = 1, rate = 5)#> [1] 1.25