Description Usage Arguments Details Value Note Examples
Beta distribution with shape parameters alpha and beta.
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)
|
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 |
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.
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)
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