| betalomax {VaRES} | R Documentation |
Beta Lomax distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the beta Lomax distribution due to Lemonte and Cordeiro (2013) given by
\begin{array}{ll}
&\displaystyle
f (x) =
\frac {\alpha}{\lambda B (a, b)} \left( 1 + \frac {x}{\lambda} \right)^{-b \alpha - 1}
\left[ 1 - \left( 1 + \frac {x}{\lambda} \right)^{-\alpha} \right]^{a - 1},
\\
&\displaystyle
F (x) = I_{1 - \left( 1 + \frac {x}{\lambda} \right)^{-\alpha}} (a, b),
\\
&\displaystyle
{\rm VaR}_p (X) = \lambda \left[ 1 - I_p^{-1} (a, b) \right]^{-1 / \alpha} - \lambda,
\\
&\displaystyle
{\rm ES}_p (X) = \frac {\lambda}{p} \int_0^p \left[ 1 - I_v^{-1} (a, b) \right]^{-1 / \alpha} dv - \lambda
\end{array}
for x > 0, 0 < p < 1, a > 0, the first shape parameter,
b > 0, the second shape parameter, \alpha > 0, the third shape parameter, and \lambda > 0, the scale parameter.
Usage
dbetalomax(x, a=1, b=1, alpha=1, lambda=1, log=FALSE)
pbetalomax(x, a=1, b=1, alpha=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
varbetalomax(p, a=1, b=1, alpha=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
esbetalomax(p, a=1, b=1, alpha=1, 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 |
a |
the value of the first scale parameter, must be positive, the default is 1 |
b |
the value of the second scale parameter, must be positive, the default is 1 |
alpha |
the value of the third 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)
dbetalomax(x)
pbetalomax(x)
varbetalomax(x)
esbetalomax(x)