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

In VGAM: Vector Generalized Linear and Additive Models

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)

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.

Details

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

Value

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

Note

This family function tries to solve a difficult problem, and the larger the data set the better. Convergence failure can commonly occur, and convergence may be very slow, so set maxit = 200, trace = TRUE, say. Inputting good initial values are advised.

This family function uses the BFGS quasi-Newton update formula for the working weight matrices. Consequently the estimated variance-covariance matrix may be inaccurate or simply wrong! The standard errors must be therefore treated with caution; these are computed in functions such as vcov() and summary().

Author(s)

T. W. Yee

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)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.