VGAM (version 1.1-12)

rec.normal: Upper Record Values from a Univariate Normal Distribution

Description

Maximum likelihood estimation of the two parameters of a univariate normal distribution when the observations are upper record values.

Usage

rec.normal(lmean = "identitylink", lsd = "loglink",
          imean = NULL, isd = NULL, imethod = 1, zero = NULL)

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

Arguments

lmean, lsd

Link functions applied to the mean and sd parameters. See Links for more choices.

imean, isd

Numeric. Optional initial values for the mean and sd. The default value NULL means they are computed internally, with the help of imethod.

imethod

Integer, either 1 or 2 or 3. Initial method, three algorithms are implemented. Choose the another value if convergence fails, or use imean and/or isd.

zero

Can be an integer vector, containing the value 1 or 2. If so, the mean or standard deviation respectively are modelled as an intercept only. Usually, setting zero = 2 will be used, if used at all. The default value NULL means both linear/additive predictors are modelled as functions of the explanatory variables. See CommonVGAMffArguments for more information.

Author

T. W. Yee

Details

The response must be a vector or one-column matrix with strictly increasing values.

References

Arnold, B. C. and Balakrishnan, N. and Nagaraja, H. N. (1998). Records, New York: John Wiley & Sons.

See Also

uninormal, double.cens.normal.

Examples

nn <- 10000; mymean <- 100
# First value is reference value or trivial record
Rdata <- data.frame(rawy = c(mymean, rnorm(nn, mymean, exp(3))))
# Keep only observations that are records:
rdata <- data.frame(y = unique(cummax(with(Rdata, rawy))))

fit <- vglm(y ~ 1, rec.normal, rdata, trace = TRUE, maxit = 200)
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)