tsp | R Documentation |
Computes the pdf, cdf, value at risk and expected shortfall for the two sided power distribution due to van Dorp and Kotz (2002) given by
\begin{array}{ll}
&\displaystyle
f (x) = \left\{ \begin{array}{ll}
\displaystyle
a \left( \frac {x}{\theta} \right)^{a - 1}, & \mbox{if $0 < x \leq \theta$,}
\\
\displaystyle
a \left( \frac {1 - x}{1 - \theta} \right)^{a - 1}, & \mbox{if $\theta < x < 1$,}
\end{array}
\right.
\\
&\displaystyle
F (x) = \left\{ \begin{array}{ll}
\displaystyle
\theta \left( \frac {x}{\theta} \right)^a, & \mbox{if $0 < x \leq \theta$,}
\\
\displaystyle
1 - (1 - \theta) \left( \frac {1 - x}{1 - \theta} \right)^a, & \mbox{if $\theta < x < 1$,}
\end{array}
\right.
\\
&\displaystyle
{\rm VaR}_p (X) = \left\{ \begin{array}{ll}
\displaystyle
\theta \left( \frac {p}{\theta} \right)^{1 / a}, & \mbox{if $0 < p \leq \theta$,}
\\
\displaystyle
1 - (1 - \theta) \left( \frac {1 - p}{1 - \theta} \right)^{1 / a}, & \mbox{if $\theta < p < 1$,}
\end{array}
\right.
\\
&\displaystyle
{\rm ES}_p (X) = \left\{ \begin{array}{ll}
\displaystyle
\frac {a \theta}{a + 1} \left( \frac {p}{\theta} \right)^{1 / a}, & \mbox{if $0 < p \leq \theta$,}
\\
\displaystyle
1 - \frac {\theta}{p} + \frac {a (2 \theta - 1)}{(a + 1) p} + \frac {a (1 - \theta)^2}{(a + 1) p}
\left( \frac {1 - p}{1 - \theta} \right)^{1 + 1 / a}, & \mbox{if $\theta < p < 1$}
\end{array}
\right.
\end{array}
for 0 < x < 1
, 0 < p < 1
, a > 0
, the shape parameter, and -\infty < \theta < \infty
, the location parameter.
dtsp(x, a=1, theta=0.5, log=FALSE)
ptsp(x, a=1, theta=0.5, log.p=FALSE, lower.tail=TRUE)
vartsp(p, a=1, theta=0.5, log.p=FALSE, lower.tail=TRUE)
estsp(p, a=1, theta=0.5)
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 |
theta |
the value of the location parameter, must take a value in the unit interval, the default is 0.5 |
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
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)
dtsp(x)
ptsp(x)
vartsp(x)
estsp(x)
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