Loglogistic distribution with shape parameter $$\tau$$ and scale parameter $$\lambda$$.

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)

## Arguments

x vector of quantiles. shape parameter $$\tau$$, must be positive rate parameter $$\beta$$, must be positive. alternative parameterization to the rate parameter, scale = 1 / rate. vector of quantiles. logical; if TRUE (default), probabilities are $$P[X \le x]$$, otherwise, $$P[X > x]$$. kth-moment. cut-off value. logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d. probability.

## 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.

## 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)#>  0.01514793
# With scale parameter
pLlogis(q = 3, shape = 3, scale = 5)#>  0.9997038
# With rate parameter
pLlogis(q = 3, shape = 3, rate = 0.2)#>  0.9997038
# Survival function
pLlogis(q = 3, shape = 3, rate = 0.2, lower.tail = FALSE)#>  0.0002962085
expValLlogis(shape = 2, scale = 4)#>  6.283185
varLlogis(shape = 3, scale = 4)#>  15.29977
kthMomentLlogis(k = 3, shape = 5, scale = 4)#>  126.8454
expValLimLlogis(d = 2, shape = 2, scale = 4)#>  1.85459
# With rate parameter
expValTruncLlogis(d = 2, shape = 2, scale = 4)#>  0.2545904
# Values greater than d
expValTruncLlogis(d = 2, shape = 2, scale = 4, less.than.d = FALSE)#>  6.028595
stopLossLlogis(d = 2, shape = 2, scale = 4)#>  4.428595
meanExcessLlogis(d = 3, shape = 2, scale = 4)#>  5.795595
# With scale parameter
VatRLlogis(kap = .2, shape = 2, scale = 4)#>  2
# With rate parameter
VatRLlogis(kap = .2, shape = 2, rate = 0.25)#>  2
# With scale parameter
TVatRLlogis(kap = .2, shape = 3, scale = 4)#>  5.588911
# With rate parameter
TVatRLlogis(kap = .2, shape = 3, rate = 0.25)#>  5.588911