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.
|
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,]