cdfemu {lmomco} | R Documentation |
Cumulative Distribution Function of the Eta-Mu Distribution
Description
This function computes the cumulative probability or nonexceedance probability of the Eta-Mu () distribution given parameters (
and
) computed by
parkmu
. The cumulative distribution function is complex and numerical integration of the probability density function pdfemu
is used or the Yacoub (2007) integral. The cumulative distribution function in terms of this integral is
where
where is the “
th-order modified Bessel function of the first kind.”
Usage
cdfemu(x, para, paracheck=TRUE, yacoubsintegral=TRUE)
Arguments
x |
A real value vector. |
para |
|
paracheck |
A logical controlling whether the parameters and checked for validity. |
yacoubsintegral |
A logical controlling whether the integral by Yacoub (2007) is used instead of numerical integration of |
Value
Nonexceedance probability () for
.
Author(s)
W.H. Asquith
References
Yacoub, M.D., 2007, The kappa-mu distribution and the eta-mu distribution: IEEE Antennas and Propagation Magazine, v. 49, no. 1, pp. 68–81
See Also
pdfemu
, quaemu
, lmomemu
, paremu
Examples
para <- vec2par(c(0.5, 1.4), type="emu")
cdfemu(1.2, para, yacoubsintegral=TRUE)
cdfemu(1.2, para, yacoubsintegral=FALSE)
## Not run:
delx <- 0.01; x <- seq(0,3, by=delx)
nx <- 20*log10(x)
plot(c(-30,10), 10^c(-3,0), log="y", xaxs="i", yaxs="i",
xlab="RHO", ylab="cdfemu(RHO)", type="n")
m <- 0.75
mus <- c(0.7425, 0.7125, 0.675, 0.6, 0.5, 0.45)
for(mu in mus) {
eta <- sqrt((m / (2*mu))^-1 - 1)
lines(nx, cdfemu(x, vec2par(c(eta, mu), type="emu")))
}
mtext("Yacoub (2007, figure 8)")
# Now add some last boundary lines
mu <- m; eta <- sqrt((m / (2*mu))^-1 - 1)
lines(nx, cdfemu(x, vec2par(c(eta, mu), type="emu")), col=8, lwd=4)
mu <- m/2; eta <- sqrt((m / (2*mu))^-1 - 1)
lines(nx, cdfemu(x, vec2par(c(eta, mu), type="emu")), col=4, lwd=2, lty=2)
delx <- 0.01; x <- seq(0,3, by=delx)
nx <- 20*log10(x)
m <- 0.75; col <- 4; lty <- 2
plot(c(-30,10), 10^c(-3,0), log="y", xaxs="i", yaxs="i",
xlab="RHO", ylab="cdfemu(RHO)", type="n")
for(mu in c(m/2,seq(m/2+0.01,m,by=0.01), m-0.001, m)) {
if(mu > 0.67) { col <- 2; lty <- 1 }
eta <- sqrt((m / (2*mu))^-1 - 1)
lines(nx, cdfemu(x, vec2par(c(eta, mu), type="emu")),
col=col, lwd=.75, lty=lty)
}
## End(Not run)