genunif | R Documentation |
Computes the pdf, cdf, value at risk and expected shortfall for the generalized uniform distribution given by
\begin{array}{ll}
&\displaystyle
f (x) = h k c (x - a)^{c - 1} \left[ 1 - k (x - a)^c \right]^{h - 1},
\\
&\displaystyle
F (x) = 1 - \left[ 1 - k (x - a)^c \right]^h,
\\
&\displaystyle
{\rm VaR}_p (X) = a + k^{-1/c} \left[ 1 - (1 - p)^{1/h} \right]^{1/c},
\\
&\displaystyle
{\rm ES}_p (X) = a + \frac {k^{-1/c}}{p} \int_0^p \left[ 1 - (1 - v)^{1/h} \right]^{1/c} dv
\end{array}
for a \leq x \leq a + k^{-1/c}
, 0 < p < 1
, -\infty < a < \infty
, the location parameter, c > 0
, the first shape parameter, k > 0
, the scale parameter, and h > 0
, the second shape parameter.
dgenunif(x, a=0, c=1, h=1, k=1, log=FALSE)
pgenunif(x, a=0, c=1, h=1, k=1, log.p=FALSE, lower.tail=TRUE)
vargenunif(p, a=0, c=1, h=1, k=1, log.p=FALSE, lower.tail=TRUE)
esgenunif(p, a=0, c=1, h=1, k=1)
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 |
a |
the value of the location parameter, can take any real value, the default is zero |
k |
the value of the scale parameter, must be positive, the default is 1 |
c |
the value of the first scale parameter, must be positive, the default is 1 |
h |
the value of the second 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 |
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
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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/03610918.2014.944658")}
x=runif(10,min=0,max=1)
dgenunif(x)
pgenunif(x)
vargenunif(x)
esgenunif(x)
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