| rayleigh {VGAM} | R Documentation |
Estimating the parameter of the Rayleigh distribution by maximum likelihood estimation. Right-censoring is allowed.
rayleigh(link = "loge", earg=list(), nrfs=1/3+0.01) crayleigh(link ="loge", earg=list(), expected=FALSE)
link |
Parameter link function applied to the parameter a.
See Links for more choices.
A log link is the default because a is positive.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
nrfs |
Numeric, of length one, with value in [0,1].
Weighting factor between Newton-Raphson and Fisher scoring.
The value 0 means pure Newton-Raphson, while 1 means pure Fisher scoring.
The default value uses a mixture of the two algorithms, and retaining
positive-definite working weights.
|
expected |
Logical. For censored data only, FALSE
means the Newton-Raphson algorithm, and TRUE means Fisher scoring.
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The Rayleigh distribution, which is used in physics, has a probability density function that can be written
f(y) = y*exp(-0.5*(y/a)^2)/a^2
for y>0 and a>0. The mean of Y is a * sqrt(pi / 2) and its variance is a^2 (4-pi)/2.
The VGAM family function crayleigh handles right-censored
data (the true value is greater than the observed value). To indicate
which type of censoring, input extra = list(rightcensored = vec2)
where vec2 is a logical vector the same length as the response.
If the component of this list is missing then the logical values are
taken to be FALSE. The fitted object has this component stored
in the extra slot.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm
and vgam.
The theory behind the argument expected is not fully complete.
A related distribution is the Maxwell distribution.
T. W. Yee
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
n = 1000; a = exp(2) ystar = rrayleigh(n, a=a) fit = vglm(ystar ~ 1, rayleigh, trace=TRUE, crit="c") fitted(fit)[1:5] mean(ystar) coef(fit, matrix=TRUE) Coef(fit) # Censored data U = runif(n, 5, 15) y = pmin(U, ystar) ## Not run: par(mfrow=c(1,2)); hist(ystar); hist(y) ## End(Not run) extra = list(rightcensored = ystar > U) fit = vglm(y ~ 1, crayleigh, trace=TRUE, extra=extra) table(fit@extra$rightcen) coef(fit, matrix=TRUE) fitted(fit)[1:4,]