Description Usage Arguments Value Author(s) References Examples

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.

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`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 |

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`

.

Saralees Nadarajah

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

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