Description Usage Arguments Value Author(s) References Examples

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

*\begin{array}{ll}
&\displaystyle
f (x) = \frac {1}{σ} \exp ≤ft( -\frac {x - μ}{σ} \right)
≤ft[ 1 + \exp ≤ft( -\frac {x - μ}{σ} \right) \right]^{-2},
\\
&\displaystyle
F (x) = \frac {1}{1 + \exp ≤ft( -\frac {x - μ}{σ} \right)},
\\
&\displaystyle
{\rm VaR}_p (X) = μ + σ \log ≤ft[ p (1 - p) \right],
\\
&\displaystyle
{\rm ES}_p (X) = μ - 2 σ + σ \log p - σ \frac {1 - p}{p} \log (1 - p)
\end{array}*

for *-∞ < x < ∞*, *0 < p < 1*, *-∞ < μ < ∞*, the location parameter, and *σ > 0*, the scale parameter.

1 2 3 4 |

`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 |

`mu` |
the value of the location parameter, can take any real value, the default is zero |

`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)
dlogistic(x)
plogistic(x)
varlogistic(x)
eslogistic(x)
``` |

VaRES documentation built on May 29, 2017, 8:27 p.m.

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