Weibull: Weibull Distribution

In Distributacalcul: Probability Distribution Functions

Description

Weibull distribution with shape parameter tau and rate parameter beta.

Usage

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

# 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.