# HL: Hankin-Lee distribution

Description Usage Arguments Value Author(s) References Examples

### Description

Computes the pdf, cdf, value at risk and expected shortfall for the Hankin-Lee distribution due to Hankin and Lee (2006) given by

\begin{array}{ll} &\displaystyle {\rm VaR}_p (X) = \frac {c p^a}{(1 - p)^b}, \\ &\displaystyle {\rm ES}_p (X) = \frac {c}{p} B_p (a + 1, 1 - b) \end{array}

for 0 < p < 1, c > 0, the scale parameter, a > 0, the first shape parameter, and b > 0, the second shape parameter.

### Usage

 1 2 varHL(p, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE) esHL(p, a=1, b=1, c=1) 

### Arguments

 p scaler or vector of values at which the value at risk or expected shortfall needs to be computed c the value of the scale parameter, must be positive, the default is 1 a the value of the first shape parameter, must be positive, the default is 1 b the value of the second 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 x=runif(10,min=0,max=1) varHL(x) esHL(x) 

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