Weibull: Weibull Distribution In Distributacalcul: Probability Distribution Functions

Description

Weibull distribution with shape parameter tau and rate parameter beta.

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```expValWeibull(shape, rate = 1/scale, scale = 1/rate) varWeibull(shape, rate = 1/scale, scale = 1/rate) kthMomentWeibull(k, shape, rate = 1/scale, scale = 1/rate) expValLimWeibull(d, shape, rate = 1/scale, scale = 1/rate) expValTruncWeibull( d, shape, rate = 1/scale, scale = 1/rate, less.than.d = TRUE ) stopLossWeibull(d, shape, rate = 1/scale, scale = 1/rate) meanExcessWeibull(d, shape, rate = 1/scale, scale = 1/rate) VatRWeibull(kap, shape, rate = 1/scale, scale = 1/rate) TVatRWeibull(kap, shape, rate = 1/scale, scale = 1/rate) ```

Arguments

 `shape` shape parameter tau, must be positive `rate` rate parameter beta, must be positive. `scale` alternative parameterization to the rate parameter, scale = 1 / rate. `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.

Details

The Weibull distribution with shape parameter t and rate parameter b has density:

f(x) = b t (b x)^(t - 1) e^{(-b x)^t}

for x > 0, b > 0, t > 0

Value

Function :

• `expValWeibull` gives the expected value.

• `varWeibull` gives the variance.

• `kthMomentWeibull` gives the kth moment.

• `expValLimWeibull` gives the limited mean.

• `expValTruncWeibull` gives the truncated mean.

• `stopLossWeibull` gives the stop-loss.

• `meanExcessWeibull` gives the mean excess loss.

• `VatRWeibull` gives the Value-at-Risk.

• `TVatRWeibull` gives the Tail Value-at-Risk.

Invalid parameter values will return an error detailing which parameter is problematic.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56``` ```# With scale parameter expValWeibull(shape = 2, scale = 5) # With rate parameter expValWeibull(shape = 2, rate = 0.2) # With scale parameter varWeibull(shape = 2, scale = 5) # With rate parameter varWeibull(shape = 2, rate = 0.2) # With scale parameter kthMomentWeibull(k = 2, shape = 2, scale = 5) # With rate parameter kthMomentWeibull(k = 2, shape = 2, rate = 0.2) # With scale parameter expValLimWeibull(d = 2, shape = 2, scale = 5) # With rate parameter expValLimWeibull(d = 2, shape = 2, rate = 0.2) # With scale parameter expValTruncWeibull(d = 2, shape = 2, scale = 5) # With rate parameter expValTruncWeibull(d = 2, shape = 2, rate = 0.2) # Mean of values greater than d expValTruncWeibull(d = 2, shape = 2, rate = 0.2, less.than.d = FALSE) # With scale parameter stopLossWeibull(d = 2, shape = 3, scale = 4) # With rate parameter stopLossWeibull(d = 2, shape = 3, rate = 0.25) # With scale parameter meanExcessWeibull(d = 2, shape = 3, scale = 4) # With rate parameter meanExcessWeibull(d = 2, shape = 3, rate = 0.25) # With scale parameter VatRWeibull(kap = .2, shape = 3, scale = 4) # With rate parameter VatRWeibull(kap = .2, shape = 3, rate = 0.25) # With scale parameter TVatRWeibull(kap = .2, shape = 3, scale = 4) # With rate parameter TVatRWeibull(kap = .2, shape = 3, rate = 0.25) ```

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