Distributacalcul (version 0.4.0)

llogis: Loglogistic Distribution

Description

Loglogistic distribution with shape parameter \(\tau\) and scale parameter \(\lambda\).

Usage

dLlogis(x, shape, rate = 1/scale, scale = 1/rate)
pLlogis(q, shape, rate = 1/scale, scale = 1/rate, lower.tail = TRUE)
expValLlogis(shape, rate = 1/scale, scale = 1/rate)
varLlogis(shape, rate = 1/scale, scale = 1/rate)
kthMomentLlogis(k, shape, rate = 1/scale, scale = 1/rate)
expValLimLlogis(d, shape, rate = 1/scale, scale = 1/rate)
expValTruncLlogis(d, shape, rate = 1/scale, scale = 1/rate, less.than.d = TRUE)
stopLossLlogis(d, shape, rate = 1/scale, scale = 1/rate)
meanExcessLlogis(d, shape, rate = 1/scale, scale = 1/rate)
VatRLlogis(kap, shape, rate = 1/scale, scale = 1/rate)
TVatRLlogis(kap, shape, rate = 1/scale, scale = 1/rate)

Value

Function :

• dLlogis gives the probability density function (PDF).

• pLlogis gives the cumulative density function (CDF).

• expValLlogis gives the expected value.

• varLlogis gives the variance.

• kthMomentLlogis gives the kth moment.

• expValLimLlogis gives the limited mean.

• expValTruncLlogis gives the truncated mean.

• stopLossLlogis gives the stop-loss.

• meanExcessLlogis gives the mean excess loss.

• VatRLlogis gives the Value-at-Risk.

• TVatRLlogis gives the Tail Value-at-Risk.

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

Arguments

x, q

vector of quantiles.

shape

shape parameter \(\tau\), must be positive

rate

rate parameter \(\beta\), must be positive.

scale

alternative parameterization to the rate parameter, scale = 1 / rate.

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

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 loglogistic distribution with shape parameter \(\tau\) and scale parameter \(\lambda\) has density: $$\frac{\tau \lambda^\tau x^{\tau -1}}{(\lambda^{\tau }+x^{\tau })^{2}}$$ for \(x \in \mathcal{R}^+\), \(\lambda, \tau > 0\).

Examples

dLlogis(x = 2, shape = 2, scale = 4)

# With scale parameter
pLlogis(q = 3, shape = 3, scale = 5)

# With rate parameter
pLlogis(q = 3, shape = 3, rate = 0.2)

# Survival function
pLlogis(q = 3, shape = 3, rate = 0.2, lower.tail = FALSE)

expValLlogis(shape = 2, scale = 4)

varLlogis(shape = 3, scale = 4)

kthMomentLlogis(k = 3, shape = 5, scale = 4)

expValLimLlogis(d = 2, shape = 2, scale = 4)

# With rate parameter
expValTruncLlogis(d = 2, shape = 2, scale = 4)

# Values greater than d
expValTruncLlogis(d = 2, shape = 2, scale = 4, less.than.d = FALSE)

stopLossLlogis(d = 2, shape = 2, scale = 4)

meanExcessLlogis(d = 3, shape = 2, scale = 4)

# With scale parameter
VatRLlogis(kap = .2, shape = 2, scale = 4)

# With rate parameter
VatRLlogis(kap = .2, shape = 2, rate = 0.25)

# With scale parameter
TVatRLlogis(kap = .2, shape = 3, scale = 4)

# With rate parameter
TVatRLlogis(kap = .2, shape = 3, rate = 0.25)