Computes the pdf, cdf, value at risk and expected shortfall for the beta Pareto distribution due to Akinsete et al. (2008) given by [REMOVE_ME]\displaystylef(x)=B(c,d)aKadx−ad−1[1−(xK)a]c−1,\displaystyleF(x)=I1−(xK)a(c,d),VaRp(X)=K[1−Ip−1(c,d)]−1/a,ESp(X)=pK∫0p[1−Iv−1(c,d)]−1/adv[REMOVEME2]
for x≥K, 0<p<1, K>0, the scale parameter, a>0, the first shape parameter, c>0, the second shape parameter, and d>0, the third shape parameter.
Description
Computes the pdf, cdf, value at risk and expected shortfall for the beta Pareto distribution due to Akinsete et al. (2008) given by
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
K: the value of the scale parameter, must be positive, the default is 1
a: the value of the first shape parameter, must be positive, the default is 1
c: the value of the second shape parameter, must be positive, the default is 1
d: the value of the third shape 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")