BS {VaRES} | R Documentation |
Birnbaum-Saunders distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the Birnbaum-Saunders distribution due to Birnbaum and Saunders (1969a, 1969b) given by
for ,
, and
, the scale parameter.
Usage
dBS(x, gamma=1, log=FALSE)
pBS(x, gamma=1, log.p=FALSE, lower.tail=TRUE)
varBS(p, gamma=1, log.p=FALSE, lower.tail=TRUE)
esBS(p, gamma=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 |
gamma |
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 |
Value
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
.
Author(s)
Saralees Nadarajah
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, doi:10.1080/03610918.2014.944658
Examples
x=runif(10,min=0,max=1)
dBS(x)
pBS(x)
varBS(x)
esBS(x)