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.

shape2

shape parameter \(\beta\), must be positive.

k

kth-moment.

d

cut-off value.

less.than.d

logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.

kap

probability.

t

t.

k0

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