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)

## Arguments

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.

## Value

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.

## Details

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 $$x \in \mathcal{R}^+$$, $$\beta > 0$$.

## Note

Function VatRExp is a wrapper of the qexp function from the stats package.

## Examples

# 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