Beta {Distributacalcul}

Beta Distribution

Description

Beta distribution with shape parameters \alpha and \beta.

Usage

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.

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.

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.

Note

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

Examples

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)