halflogis function

Half logistic distribution

Computes the pdf, cdf, value at risk and expected shortfall for the half logistic distribution given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {2 \lambda \exp \left( -\lambda x \right)}{\left[ 1 + \exp \left( -\lambda x \right) \right]^2},\\&\displaystyleF (x) = \frac {1 - \exp \left( -\lambda x \right)}{1 + \exp \left( -\lambda x \right)},\\&\displaystyle{\rm VaR}_p (X) = -\frac {1}{\lambda} \log \frac {1 - p}{1 + p},\\&\displaystyle{\rm ES}_p (X) = -\frac {1}{\lambda} \log \frac {1 - p}{1 + p} + \frac {1}{\lambda p} \log \left( 1 - p^2 \right)\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, and $\lambda > 0$, the scale parameter.

Description

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

for $x > 0$, $0 < p < 1$, and $\lambda > 0$, the scale parameter.

dhalflogis(x, lambda=1, log=FALSE)
phalflogis(x, lambda=1, log.p=FALSE, lower.tail=TRUE)
varhalflogis(p, lambda=1, log.p=FALSE, lower.tail=TRUE)
eshalflogis(p, lambda=1)

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
• lambda: 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

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)
dhalflogis(x)
phalflogis(x)
varhalflogis(x)
eshalflogis(x)