secant function

Hyperbolic secant distribution

Computes the pdf, cdf, value at risk and expected shortfall for the hyperbolic secant distribution given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {1}{2} {\rm sech} \left( \frac {\pi x}{2} \right),\\&\displaystyleF (x) = \frac {2}{\pi} \arctan \left[ \exp \left( \frac {\pi x}{2} \right) \right],\\&\displaystyle{\rm VaR}_p (X) = \frac {2}{\pi} \log \left[ \tan \left( \frac {\pi p}{2} \right) \right],\\&\displaystyle{\rm ES}_p (X) = \frac {2}{\pi p} \int_0^p \log \left[ \tan \left( \frac {\pi v}{2} \right) \right] dv\end{array} [REMOVE_ME_2]$

for $-\infty < x < \infty$, and $0 < p < 1$.

Description

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

for $-\infty < x < \infty$, and $0 < p < 1$.

dsecant(x, log=FALSE)
psecant(x, log.p=FALSE, lower.tail=TRUE)
varsecant(p, log.p=FALSE, lower.tail=TRUE)
essecant(p)

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
• 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

Returns

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

Stephen Chan, Saralees Nadarajah & Emmanuel Afuecheta (2016). An R Package for Value at Risk and Expected Shortfall, Communications in Statistics - Simulation and Computation, 45:9, 3416-3434, tools:::Rd_expr_doi("10.1080/03610918.2014.944658")

Author(s)

Saralees Nadarajah

Examples

x=runif(10,min=0,max=1)
dsecant(x)
psecant(x)
varsecant(x)
essecant(x)