Beta: Beta Distribution
In Distributacalcul: Probability Distribution Functions

Description Usage Arguments Details Value Note Examples

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)

`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.

The Beta distribution with shape parameters a and b has density:

f(x) = Γ(a+b) / (Γ(a)Γ(b))x^(a - 1)(1 - x)^(b - 1)

for 0 ≤ x ≤ 1, a, b > 0.

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.

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

expValBeta(shape1 = 3, shape2 = 5)

varBeta(shape1 = 4, shape2 = 5)

kthMomentBeta(k = 3, shape1 = 4, shape2 = 5)

expValLimBeta(d = 0.3, shape1 = 4, shape2 = 5)

expValTruncBeta(d = 0.4, shape1 = 4, shape2 = 5)

# Values less than d
expValTruncBeta(d = 0.4, shape1 = 4, shape2 = 5, less.than.d = FALSE)

stopLossBeta(d = 0.3, shape1 = 4, shape2 = 5)

meanExcessBeta(d = .3, shape1 = 4, shape2 = 5)

VatRBeta(kap = .99, shape1 = 4, shape2 = 5)

TVatRBeta(kap = .99, shape1 = 4, shape2 = 5)

mgfBeta(t = 1, shape1 = 3, shape2 = 5, k0 = 1E2)