Description Usage Arguments Value Author(s) References Examples

Computes the pdf, cdf, value at risk and expected shortfall for the half Cauchy distribution given by

*\begin{array}{ll}
&\displaystyle
f (x) = \frac {2}{π} \frac {σ}{x^2 + σ^2},
\\
&\displaystyle
F (x) = \frac {2}{π} \arctan ≤ft( \frac {x}{σ} \right),
\\
&\displaystyle
{\rm VaR}_p (X) = σ \tan ≤ft( \frac {π p}{2} \right),
\\
&\displaystyle
{\rm ES}_p (X) = \frac {σ}{p} \int_0^p \tan ≤ft( \frac {π v}{2} \right) dv
\end{array}*

for *x > 0*, *0 < p < 1*, and *σ > 0*, the scale parameter.

1 2 3 4 | ```
dhalfcauchy(x, sigma=1, log=FALSE)
phalfcauchy(x, sigma=1, log.p=FALSE, lower.tail=TRUE)
varhalfcauchy(p, sigma=1, log.p=FALSE, lower.tail=TRUE)
eshalfcauchy(p, sigma=1)
``` |

`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 |

`sigma` |
the value of the scale 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

1 2 3 4 5 | ```
x=runif(10,min=0,max=1)
dhalfcauchy(x)
phalfcauchy(x)
varhalfcauchy(x)
eshalfcauchy(x)
``` |

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