Upper Record Values from a Univariate Normal Distribution
Maximum likelihood estimation of the two parameters of a univariate normal distribution when the observations are upper record values.
rec.normal(lmean = "identitylink", lsd = "loglink",
imean = NULL, isd = NULL, imethod = 1, zero = NULL)lmean, lsd |
Link functions applied to the mean and sd parameters.
See |
imean, isd |
Numeric. Optional initial values for the mean and sd.
The default value |
imethod |
Integer, either 1 or 2 or 3. Initial method, three algorithms are
implemented. Choose the another value if convergence fails, or use
|
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 |
The response must be a vector or one-column matrix with strictly increasing values.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
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().
T. W. Yee
Arnold, B. C. and Balakrishnan, N. and Nagaraja, H. N. (1998). Records, New York: John Wiley & Sons.
nn <- 10000; mymean <- 100 # First value is reference value or trivial record Rdata <- data.frame(rawy = c(mymean, rnorm(nn, me = mymean, sd = exp(3)))) # Keep only observations that are records: rdata <- data.frame(y = unique(cummax(with(Rdata, rawy)))) fit <- vglm(y ~ 1, rec.normal, data = rdata, trace = TRUE, maxit = 200) coef(fit, matrix = TRUE) Coef(fit) summary(fit)
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