MADCI {DescTools}

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 <[e-mail]> (only interface)

References

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

See Also

mad, MAD

Examples

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

MADCI(x)                           # single sample

MADCI(x, y)                        # two sample difference
MADCI(x, y, two.samp.diff = FALSE) # two sample squared ratio