lomax | R Documentation |
Computes the pdf, cdf, value at risk and expected shortfall for the Lomax distribution due to Lomax (1954) given by
\begin{array}{ll}
&\displaystyle
f (x) = \frac {a}{\lambda} \left( 1 + \frac {x}{\lambda} \right)^{-a - 1},
\\
&\displaystyle
F (x) = 1 - \left( 1 + \frac {x}{\lambda} \right)^{-a},
\\
&\displaystyle
{\rm VaR}_p (X) = \lambda \left[ (1 - p)^{-1 / a} - 1 \right],
\\
&\displaystyle
{\rm ES}_p (X) = -\lambda + \frac {\lambda - \lambda (1 - p)^{1 - 1 / a}}{p - p / a}
\end{array}
for x > 0
, 0 < p < 1
, a > 0
, the shape parameter, and \lambda > 0
, the scale parameter.
dlomax(x, a=1, lambda=1, log=FALSE)
plomax(x, a=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
varlomax(p, a=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
eslomax(p, a=1, lambda=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 |
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
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)
dlomax(x)
plomax(x)
varlomax(x)
eslomax(x)
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