Computes the pdf, cdf, value at risk and expected shortfall for the exponential extension distribution due to Nadarajah and Haghighi (2011) given by
\begin{array}{ll} &\displaystyle f (x) = a λ (1 + λ x)^{a - 1} \exp ≤ft[ 1 - (1 + λ x)^a \right], \\ &\displaystyle F (x) = 1 - \exp ≤ft[ 1 - (1 + λ x)^a \right], \\ &\displaystyle {\rm VaR}_p (X) = \frac {≤ft[ 1 - \log (1 - p) \right]^{1 / a} - 1}{λ}, \\ &\displaystyle {\rm ES}_p (X) = -\frac {1}{λ} + \frac {1}{λ p} \int_0^p ≤ft[ 1 - \log (1 - v) \right]^{1 / a} dv \end{array}
for x > 0, 0 < p < 1, a > 0, the shape parameter and λ > 0, the scale parameter.
1 2 3 4 |
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 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 |
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
.
Saralees Nadarajah
S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted
1 2 3 4 5 |
Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
All documentation is copyright its authors; we didn't write any of that.