Plotting 2D confidence sets for normal mean and variance

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Description

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

Usage

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plotMV2D(dat, n, method, alpha=0.1, scale="var", axnames=NULL,
                main="Title", xlim=NULL, ylim=NULL, col="black", steps=400)

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".

axnames

A vector of two character strings giving the x and y axis labels. Default is NULL.

main

A character string giving the plot title.

xlim

A numeric vector of length two specifying the plotting range on the x-axis. Default is NULL.

ylim

A numeric vector of length two specifying the plotting range on the y-axis. Default is NULL.

col

A character string specifying the colour of the plotted region or intervals.

steps

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

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

A graphical display of a (simultaneous) confidence set in two dimensions.

Note

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

Author(s)

Philip Pallmann (p.pallmann@lancaster.ac.uk) using code from xxxxx

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

plot2D for confidence regions and intervals around (multivariate) normal means.

Examples

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## Not run: 
# Generate normal data

mydata <- rnorm(n=50)

# Plot simultaneous 90

plotMV2D(dat=mydata, method="mood", alpha=0.1, main="Mood")
plotMV2D(dat=mydata, method="large", alpha=0.1, main="Large-sample")
plotMV2D(dat=mydata, method="plugin", alpha=0.1, main="Plug-in")
plotMV2D(dat=mydata, method="pluginF", alpha=0.1, main="Plug-in (F distribution)")
plotMV2D(dat=mydata, method="lrt", alpha=0.1, main="Likelihood ratio test")

## End(Not run)