csetMV {jocre}

Confidence regions and intervals for a normal mean and variance

Description

Computes boundaries of (simultaneous) confidence regions for the mean and variance of a normal distribution using different methods.

Usage

csetMV(dat, n, method, alpha=0.1, scale="var", steps=500)

Arguments

dat

A vector of numeric values assumed to follow a normal distribution. Not required for method="cheng.iles" or "min.area".

n

A numeric value giving the sample size. Only required for method="cheng.iles" or "min.area".

method

A character string specifying the method to be used. See details for available methods.

alpha

A numeric value giving the type I error level to be controlled. Default is 0.1.

scale

A character string specifying whether the variance (var) or standard deviation (sd) is to be plotted on the y axis. Not required for method="cheng.iles" or "min.area".

steps

An integer setting the initial number of steps for the search algorithm. Default is 800.

Details

Available methods are: mood for the classical region described in Mood (1950); large for the large-sample approximation region described in section 4.1 of Arnold & Shavelle (1998); plugin for a plug-in variant of the large-sample approximation region described in section 4.2 of Arnold & Shavelle (1998); pluginF for the plug-in variant of the large-sample approximation region described in section 4.3 of Arnold & Shavelle (1998) using an asymptotic F distribution as in Douglas (1993); lrt for the likelihood ratio test region described in section 4.4 of Arnold & Shavelle (1998); cheng.iles for the region described in Cheng & Iles (1983); min.area for the minimum-area region described in Frey et al. (2009).

Value

An object of class JOCMV.

Note

Warning: please use with care! Some of the functionality has not yet been thoroughly tested.

Author(s)

Philip Pallmann ([e-mail])

References

Barry C. Arnold & Robert M. Shaville (1998) Joint confidence sets for the mean and variance of a normal distribution. The American Statistician, 52(2), 133–140.

R. C. H. Cheng & T. C. Iles (1983) Confidence bands for cumulative distribution functions of continuous random variables. Technometrics, 25(1), 77–86.

J. B. Douglas (1993) Confidence regions for parameter pairs. The American Statistician, 47(1), 43–45.

Jesse Frey, Osvaldo Marrero, Douglas Norton (2009) Minimum-area confidence sets for a normal distribution. Journal of Statistical Planning and Inference, 139(3), 1023–1032.

Alexander M. Mood (1950) Introduction to the Theory of Statistics. McGraw-Hill, New York, NY.

See Also

cset for (simultaneous) confidence regions and intervals around multivariate normal means.

Examples

## Not run: 
# Simultaneous 90% confidence regions for the mean and variance or sd of univariate normal data

univar <- rnorm(n=50)

moodvar <- csetMV(dat=univar, method="mood", alpha=0.1, scale="var")
summary(moodvar)
plot(moodvar)

moodsd <- csetMV(dat=univar, method="mood", alpha=0.1, scale="sd")
summary(moodsd)
plot(moodsd)

## End(Not run)