# Hlogis: Hosking logistic distribution

Description Usage Arguments Value Author(s) References Examples

### Description

Computes the pdf, cdf, value at risk and expected shortfall for the Hosking logistic distribution due to Hosking (1989, 1990) given by

\begin{array}{ll} &\displaystyle f (x) = \frac {(1 - k x)^{1 / k - 1}}{≤ft[ 1 + (1 - k x)^{1 / k} \right]^2}, \\ &\displaystyle F (x) = \frac {1}{1 + (1 - k x)^{1 / k}}, \\ &\displaystyle {\rm VaR}_p (X) = \frac {1}{k} ≤ft[ 1 - ≤ft( \frac {1 - p}{p} \right)^k \right], \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{k} - \frac {1}{kp} B_p (1 - k, 1 + k) \end{array}

for x < 1/k if k > 0, x > 1/k if k < 0, -∞ < x < ∞ if k = 0, and -∞ < k < ∞, the shape parameter.

### Usage

 1 2 3 4 dHlogis(x, k=1, log=FALSE) pHlogis(x, k=1, log.p=FALSE, lower.tail=TRUE) varHlogis(p, k=1, log.p=FALSE, lower.tail=TRUE) esHlogis(p, k=1) 

### Arguments

 x scaler or vector of values at which the pdf or cdf needs to be computed p scaler or vector of values at which the value at risk or expected shortfall needs to be computed k the value of the shape parameter, must be positive, the default is 1 log if TRUE then log(pdf) are returned log.p if TRUE then log(cdf) are returned and quantiles are computed for exp(p) lower.tail if FALSE then 1-cdf are returned and quantiles are computed for 1-p

### Value

An object of the same length as x, giving the pdf or cdf values computed at x or an object of the same length as p, giving the values at risk or expected shortfall computed at p.

### References

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

### Examples

 1 2 3 4 5 x=runif(10,min=0,max=1) dHlogis(x) pHlogis(x) varHlogis(x) esHlogis(x) 

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