Rayleigh Regression Family Function
Estimating the parameter of the Rayleigh distribution by maximum likelihood estimation. Right-censoring is allowed.
rayleigh(lscale = "loglink", nrfs = 1/3 + 0.01,
oim.mean = TRUE, zero = NULL, parallel = FALSE,
type.fitted = c("mean", "percentiles", "Qlink"),
percentiles = 50)
cens.rayleigh(lscale = "loglink", oim = TRUE)lscale |
Parameter link function applied to the scale parameter b.
See |
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. |
oim.mean |
Logical, used only for intercept-only models.
|
oim |
Logical.
For censored data only,
|
zero, parallel |
Details at |
type.fitted, percentiles |
See |
The Rayleigh distribution, which is used in physics, has a probability density function that can be written
f(y) = y*exp(-0.5*(y/b)^2)/b^2
for y > 0 and b > 0. The mean of Y is b * sqrt(pi / 2) (returned as the fitted values) and its variance is b^2 (4-pi)/2.
The VGAM family function cens.rayleigh 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.
The VGAM family function rayleigh handles multiple
responses.
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 oim is not fully complete.
The poisson.points family function is
more general so that if ostatistic = 1 and dimension = 2
then it coincides with rayleigh.
Other related distributions are the Maxwell
and Weibull distributions.
T. W. Yee
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
nn <- 1000; Scale <- exp(2)
rdata <- data.frame(ystar = rrayleigh(nn, scale = Scale))
fit <- vglm(ystar ~ 1, rayleigh, data = rdata, trace = TRUE)
head(fitted(fit))
with(rdata, mean(ystar))
coef(fit, matrix = TRUE)
Coef(fit)
# Censored data
rdata <- transform(rdata, U = runif(nn, 5, 15))
rdata <- transform(rdata, y = pmin(U, ystar))
## Not run: par(mfrow = c(1, 2))
hist(with(rdata, ystar)); hist(with(rdata, y))
## End(Not run)
extra <- with(rdata, list(rightcensored = ystar > U))
fit <- vglm(y ~ 1, cens.rayleigh, data = rdata, trace = TRUE,
extra = extra, crit = "coef")
table(fit@extra$rightcen)
coef(fit, matrix = TRUE)
head(fitted(fit))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.