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)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.
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.
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 \(x \in [0, 1]\), \(\alpha, \beta > 0\).
Function VatRBeta is a wrapper for the qbeta
function from the stats package.
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