Rayleigh {VGAM} | R Documentation |
Density, distribution function, quantile function and random
generation for the Rayleigh distribution with parameter
a
.
drayleigh(x, a) prayleigh(q, a) qrayleigh(p, a) rrayleigh(n, a)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. Must be a positive integer of length 1. |
a |
the parameter a. |
See rayleigh
, the VGAM family function
for estimating the parameter a by maximum likelihood estimation,
for the formula of the probability density function and range restrictions
on the parameter a.
drayleigh
gives the density,
prayleigh
gives the distribution function,
qrayleigh
gives the quantile function, and
rrayleigh
generates random deviates.
The Rayleigh distribution is related to the Maxwell distribution.
T. W. Yee
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
## Not run: a = 2 x = seq(-1, 8, by=0.1) plot(x, drayleigh(x, a=a), type="l", ylim=c(0,1), las=1, ylab="", main="Rayleigh density divided into 10 equal areas; red=cdf") abline(h=0, col="blue", lty=2) qq = qrayleigh(seq(0.1,0.9,by=0.1),a=a) lines(qq, drayleigh(qq, a=a), col="purple", lty=3, type="h") lines(x, prayleigh(x, a=a), col="red") ## End(Not run)