| F {VaRES} | R Documentation |
F distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the F distribution given by
\begin{array}{ll}
&\displaystyle
f (x) = \frac {1}{B \left( \frac {d_1}{2}, \frac {d_2}{2} \right)}
\left( \frac {d_1}{d_2} \right)^{\frac {d_1}{2}}
x^{\frac {d_1}{2} - 1}
\left( 1 + \frac {d_1}{d_2} x \right)^{-\frac {d_1 + d_2}{2}},
\\
&\displaystyle
F (x) = I_{\frac {d_1 x}{d_1 x + d_2}} \left( \frac {d_1}{2}, \frac {d_2}{2} \right),
\\
&\displaystyle
{\rm VaR}_p (X) = \frac {d_2}{d_1} \frac {I_p^{-1} \left( \frac {d_1}{2}, \frac {d_2}{2} \right)}
{1 - I_p^{-1} \left( \frac {d_1}{2}, \frac {d_2}{2} \right)},
\\
&\displaystyle
{\rm ES}_p (X) = \frac {d_2}{d_1 p} \int_0^p
\frac {I_v^{-1} \left( \frac {d_1}{2}, \frac {d_2}{2} \right)}
{1 - I_v^{-1} \left( \frac {d_1}{2}, \frac {d_2}{2} \right)} dv
\end{array}
for x \geq K, 0 < p < 1, d_1 > 0, the first degree of freedom parameter,
and d_2 > 0, the second degree of freedom parameter.
Usage
dF(x, d1=1, d2=1, log=FALSE)
pF(x, d1=1, d2=1, log.p=FALSE, lower.tail=TRUE)
varF(p, d1=1, d2=1, log.p=FALSE, lower.tail=TRUE)
esF(p, d1=1, d2=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 |
d1 |
the value of the first degree of freedom parameter, must be positive, the default is 1 |
d2 |
the value of the second degree of freedom 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)
dF(x)
pF(x)
varF(x)
esF(x)