lfr function

Linear failure rate distribution

Computes the pdf, cdf, value at risk and expected shortfall for the linear failure rate distribution due to Bain (1974) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef(x) = (a + b x) \exp \left( -a x - b x^2 / 2 \right),\\&\displaystyleF (x) = 1 - \exp \left( -a x - b x^2 / 2 \right),\\&\displaystyle{\rm VaR}_p (X) = \frac {-a + \sqrt{a^2 - 2 b \log (1 - p)}}{b},\\&\displaystyle{\rm ES}_p (X) = -\frac {a}{b} + \frac {1}{b p} \int_0^p \sqrt{a^2 - 2 b \log (1 - v)} dv\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, $a > 0$, the first scale parameter, and $b > 0$, the second scale parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the linear failure rate distribution due to Bain (1974) given by

for $x > 0$, $0 < p < 1$, $a > 0$, the first scale parameter, and $b > 0$, the second scale parameter.

dlfr(x, a=1, b=1, log=FALSE)
plfr(x, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
varlfr(p, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
eslfr(p, a=1, 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
• a: the value of the first scale parameter, must be positive, the default is 1
• b: 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

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)
dlfr(x)
plfr(x)
varlfr(x)
eslfr(x)