# llogis: Loglogistic Distribution In Distributacalcul: Probability Distribution Functions

## Description

Loglogistic distribution with shape parameter tau and scale parameter lambda.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```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` shape parameter tau, must be positive `rate` rate parameter beta, must be positive. `scale` alternative parameterization to the rate parameter, scale = 1 / rate. `q` vector of quantiles. `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ 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 t and scale parameter lam has density:

f(x) = t lam^t x^(t - 1) / (lam^t + x^t)^2

for x > 0, lam, t > 0.

## 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.

## 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``` ```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) ```

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