## Confidence Intervals for Median Absolute Deviations

### Description

A function for the median absolute deviation is included in base R, mad, but there's no function for calculating confidence intervals. Arachchige/Prendergast introduce interval estimators of the MAD to make reliable inferences for dispersion for a single population and ratios and differences of MADs for comparing two populations.

### Usage

MADCI(x, y = NULL, two.samp.diff = TRUE, gld.est = "TM",
conf.level = 0.95, sides = c("two.sided","left","right"),
na.rm = FALSE, ...)


### Arguments

 x a (non-empty) numeric vector of data values. y a second (non-empty) numeric vector of data values. two.samp.diff logical, defining if the confidence intervals for the difference (mad(x)-mad(y)) (default) or for the squared ratio ((mad(x)/mad(y))^2) should be calculated. Ignored if y is not given. gld.est A character string, to select the estimation method for the generalized lambda distribution. One of: ML for numerical Maximum Likelihood, MPS or MSP for Maximum Spacings Product, TM for Titterington's Method (default), SM for Starship Method, TL for method of Trimmed L-moments, Lmom for method of L-moments, DLA for the method of Distributional Least Absolutes, or Mom for method of Moments. See fit.fkml(). conf.level confidence level of the interval. sides a character string specifying the side of the confidence interval, must be one of "two.sided" (default), "left" or "right". You can specify just the initial letter. "left" would be analogue to a hypothesis of "greater" in a t.test. na.rm logical. Should missing values be removed? Defaults to FALSE. ... further arguments, not used here

### Value

a numeric vector with 3 elements:

 mad median absolute deviation lwr.ci lower bound of the confidence interval upr.ci upper bound of the confidence interval

### Author(s)

Arachchige Chandima N. P. G., Prendergast Luke A., Andri Signorell <andri@signorell.net> (only interface)

### References

Arachchige Chandima N. P. G., Prendergast Luke A. (2019) Confidence intervals for median absolute deviations, arXiv:1910.00229 [math.ST]

mad, MAD

### Examples

x <- rlnorm(100)
y <- rlnorm(200, meanlog=1.2)