Exponential 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 parameter \(\beta\), must be positive.
alternative parameterization to the rate parameter, scale = 1 / rate.
kth-moment.
cut-off value.
logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.
probability.
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: $$f\left(x\right) = \frac{1}{\beta}\textrm{e}^{-\beta x}$$ 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] 22.42068
mgfExp(t = 1, rate = 5)
#> [1] 1.25