lognorm function

Lognormal distribution

Computes the pdf, cdf, value at risk and expected shortfall for the lognormal distribution given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {1}{\sigma x} \phi \left( \frac {\log x - \mu}{\sigma} \right),\\&\displaystyleF (x) = \Phi \left( \frac {\log x - \mu}{\sigma} \right),\\&\displaystyle{\rm VaR}_p (X) = \exp \left[ \mu + \sigma \Phi^{-1} (p) \right],\\&\displaystyle{\rm ES}_p (X) = \frac {\exp (\mu)}{p} \int_0^p \exp \left[ \sigma \Phi^{-1} (v) \right] dv\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, $-\infty < \mu < \infty$, the location parameter, and $\sigma > 0$, the scale parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the lognormal distribution given by

for $x > 0$, $0 < p < 1$, $-\infty < \mu < \infty$, the location parameter, and $\sigma > 0$, the scale parameter.

dlognorm(x, mu=0, sigma=1, log=FALSE)
plognorm(x, mu=0, sigma=1, log.p=FALSE, lower.tail=TRUE)
varlognorm(p, mu=0, sigma=1, log.p=FALSE, lower.tail=TRUE)
eslognorm(p, mu=0, sigma=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
• mu: the value of the location parameter, can take any real value, the default is zero
• sigma: the value of the 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)
dlognorm(x)
plognorm(x)
varlognorm(x)
eslognorm(x)