TL2 function

Topp-Leone distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Topp-Leone distribution due to Topp and Leone (1955) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef(x) = 2 b (x (2 - x))^{b - 1} (1 - x),\\&\displaystyleF(x) = (x (2 - x))^b,\\&\displaystyle{\rm VaR}_p (X) = 1 - \sqrt{1 - p^{1 / b}},\\&\displaystyle{\rm ES}_p (X) = 1 - \frac {b}{p} B_{p^{1 / b}} \left( b, \frac {3}{2} \right)\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, and $b > 0$, the shape parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Topp-Leone distribution due to Topp and Leone (1955) given by

for $x > 0$, $0 < p < 1$, and $b > 0$, the shape parameter.

dTL2(x, b=1, log=FALSE)
pTL2(x, b=1, log.p=FALSE, lower.tail=TRUE)
varTL2(p, b=1, log.p=FALSE, lower.tail=TRUE)
esTL2(p, b=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
• b: 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

Returns

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.

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, tools:::Rd_expr_doi("10.1080/03610918.2014.944658")

Author(s)

Saralees Nadarajah

Examples

x=runif(10,min=0,max=1)
dTL2(x)
pTL2(x)
varTL2(x)
esTL2(x)