# Plotting 2D confidence sets for normal mean and variance

### Description

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

### Usage

1 2 |

### Arguments

`dat` |
A vector of numeric values assumed to follow a normal distribution. Not required for |

`n` |
A numeric value giving the sample size. Only required for |

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

`alpha` |
A numeric value giving the type I error level to be controlled. Default is |

`scale` |
A character string specifying whether the variance ( |

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

`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 |

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

`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 `method`

s 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## 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)
``` |