nakagami function

Nakagami distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Nakagami distribution due to Nakagami (1960) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {2 m^m}{\Gamma (m) a^m} x^{2 m - 1}\exp \left( -\frac {m x^2}{a} \right),\\&\displaystyleF (x) = 1 - Q \left( m, \frac {m x^2}{a} \right),\\&\displaystyle{\rm VaR}_p (X) = \sqrt{\frac {a}{m}} \sqrt{Q^{-1} (m, 1 - p)},\\&\displaystyle{\rm ES}_p (X) = \frac {\sqrt{a}}{p \sqrt{m}} \int_0^p \sqrt{Q^{-1} (m, 1 - v)} dv\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, $a > 0$, the scale parameter, and $m > 0$, the shape parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Nakagami distribution due to Nakagami (1960) given by

for $x > 0$, $0 < p < 1$, $a > 0$, the scale parameter, and $m > 0$, the shape parameter.

dnakagami(x, m=1, a=1, log=FALSE)
pnakagami(x, m=1, a=1, log.p=FALSE, lower.tail=TRUE)
varnakagami(p, m=1, a=1, log.p=FALSE, lower.tail=TRUE)
esnakagami(p, m=1, a=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 scale parameter, must be positive, the default is 1
• m: 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)
dnakagami(x)
pnakagami(x)
varnakagami(x)
esnakagami(x)