# Beta: Beta Distribution In Distributacalcul: Probability Distribution Functions

## Description

Beta distribution with shape parameters alpha and beta.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```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 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.

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```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) ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.