Beta distribution with shape parameters $$\alpha$$ and $$\beta$$.

expValBeta(shape1, shape2)

varBeta(shape1, shape2)

kthMomentBeta(k, shape1, shape2)

expValLimBeta(d, shape1, shape2)

expValTruncBeta(d, shape1, shape2, less.than.d = TRUE)

stopLossBeta(d, shape1, shape2)

meanExcessBeta(d, shape1, shape2)

VatRBeta(kap, shape1, shape2)

TVatRBeta(kap, shape1, shape2)

mgfBeta(t, shape1, shape2, k0)

## Arguments

shape1 shape parameter $$\alpha$$, must be positive. shape parameter $$\beta$$, must be positive. kth-moment. cut-off value. logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d. probability. t. point up to which to sum the distribution for the approximation.

## Value

Function :

• expValBeta gives the expected value.

• varBeta gives the variance.

• kthMomentBeta gives the kth moment.

• expValLimBeta gives the limited mean.

• expValTruncBeta gives the truncated mean.

• stopLossBeta gives the stop-loss.

• meanExcessBeta gives the mean excess loss.

• VatRBeta gives the Value-at-Risk.

• TVatRBeta gives the Tail Value-at-Risk.

• mgfBeta gives the moment generating function (MGF).

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

## Details

The Beta distribution with shape parameters $$\alpha$$ and $$\beta$$ has density: $$f\left(x\right) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha) % \Gamma(\beta)} x^{\alpha - 1} (1 - x)^(\beta - 1)$$ for $$x \in [0, 1]$$, $$\alpha, \beta > 0$$.

## Note

Function VatRBeta is a wrapper for the qbeta function from the stats package.

## Examples

expValBeta(shape1 = 3, shape2 = 5)#>  0.375
varBeta(shape1 = 4, shape2 = 5)#>  0.02469136
kthMomentBeta(k = 3, shape1 = 4, shape2 = 5)#>  0.1212121
expValLimBeta(d = 0.3, shape1 = 4, shape2 = 5)#>  4.073393
expValTruncBeta(d = 0.4, shape1 = 4, shape2 = 5)#>  0.1184745
# Values less than d
expValTruncBeta(d = 0.4, shape1 = 4, shape2 = 5, less.than.d = FALSE)#>  0.3259699
stopLossBeta(d = 0.3, shape1 = 4, shape2 = 5)#>  0.6422982
meanExcessBeta(d = .3, shape1 = 4, shape2 = 5)#>  0.1969992
VatRBeta(kap = .99, shape1 = 4, shape2 = 5)#>  0.8017979
TVatRBeta(kap = .99, shape1 = 4, shape2 = 5)#>  0.8377379
mgfBeta(t = 1, shape1 = 3, shape2 = 5, k0 = 1E2)#> Warning: This is an approximation#>  1.474362