Weibull.RdWeibull distribution with shape parameter \(\tau\) and rate parameter \(\beta\).
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)
| 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 |
| kap | probability. |
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.
The Weibull distribution with shape parameter \(\tau\) and rate parameter \(\beta\) has density: $$f\left(x\right) = \beta \tau \left( \beta x \right) ^{\tau -1} % \mathrm{e}^{-\left( \beta x\right) ^{\tau }}$$ for \(x \in \mathcal{R}^+\), \(\beta > 0\), \(\tau > 0\)
# With scale parameter expValWeibull(shape = 2, scale = 5)#> [1] 4.431135# With rate parameter expValWeibull(shape = 2, rate = 0.2)#> [1] 4.431135# With scale parameter varWeibull(shape = 2, scale = 5)#> [1] 5.365046# With rate parameter varWeibull(shape = 2, rate = 0.2)#> [1] 5.365046# With scale parameter kthMomentWeibull(k = 2, shape = 2, scale = 5)#> [1] 25# With rate parameter kthMomentWeibull(k = 2, shape = 2, rate = 0.2)#> [1] 25# With scale parameter expValLimWeibull(d = 2, shape = 2, scale = 5)#> [1] 6.135422# With rate parameter expValLimWeibull(d = 2, shape = 2, rate = 0.2)#> [1] 6.135422# With scale parameter expValTruncWeibull(d = 2, shape = 2, scale = 5)#> [1] 4.431135# With rate parameter expValTruncWeibull(d = 2, shape = 2, rate = 0.2)#> [1] 4.431135# Mean of values greater than d expValTruncWeibull(d = 2, shape = 2, rate = 0.2, less.than.d = FALSE)#> [1] 1.869292e-42# With scale parameter stopLossWeibull(d = 2, shape = 3, scale = 4)#> [1] -1.764994# With rate parameter stopLossWeibull(d = 2, shape = 3, rate = 0.25)#> [1] -1.764994# With scale parameter meanExcessWeibull(d = 2, shape = 3, scale = 4)#> [1] -2# With rate parameter meanExcessWeibull(d = 2, shape = 3, rate = 0.25)#> [1] -2# With scale parameter VatRWeibull(kap = .2, shape = 3, scale = 4)#> [1] 2.426171# With rate parameter VatRWeibull(kap = .2, shape = 3, rate = 0.25)#> [1] 2.426171# With scale parameter TVatRWeibull(kap = .2, shape = 3, scale = 4)#> [1] 4.017289# With rate parameter TVatRWeibull(kap = .2, shape = 3, rate = 0.25)#> [1] 4.017289