# acr - A C Rencher normal outlier test¶

 ACR Return critical value for test of single multivariate normal outlier using the Mahalanobis distance metric.

ACR upper percentiles critical value for test of single multivariate normal outlier.

From the method given by Wilks (1963) and approaching to a F distribution function by the Yang and Lee (1987) formulation, we compute the critical value of the maximum squared Mahalanobis distance to detect outliers from a normal multivariate sample.

We can generate all the critical values of the maximum squared Mahalanobis distance presented on the Table XXXII of by Barnett and Lewis (1978) and Table A.6 of Rencher (2002). Also with any given significance level (alpha).

Example:

>>> print("%.4f"%ACR(3, 25, 0.01))
13.1753


Created by:

A. Trujillo-Ortiz, R. Hernandez-Walls, A. Castro-Perez and K. Barba-Rojo
Facultad de Ciencias Marinas
Universidad Autonoma de Baja California
Apdo. Postal 453
Mexico.
atrujo@uabc.mx


Copyright. August 20, 2006.

To cite this file, this would be an appropriate format:

Trujillo-Ortiz, A., R. Hernandez-Walls, A. Castro-Perez and K. Barba-Rojo.
(2006). *ACR:Upper percentiles critical value for test of single
multivariate  normal outlier.* A MATLAB file. [WWW document].  URL


The function’s name is given in honour of Dr. Alvin C. Rencher for his invaluable contribution to multivariate statistics with his text ‘Methods of Multivariate Analysis’.

References:

[1] Barnett, V. and Lewis, T. (1978), Outliers on Statistical Data.
New-York:John Wiley & Sons.
[2] Rencher, A. C. (2002), Methods of Multivariate Analysis. 2nd. ed.
New-Jersey:John Wiley & Sons. Chapter 13 (pp. 408-450).
[3] Wilks, S. S. (1963), Multivariate Statistical Outliers. Sankhya,
Series A, 25: 407-426.
[4] Yang, S. S. and Lee, Y. (1987), Identification of a Multivariate
Outlier. Presented at the Annual Meeting of the American Statistical Association, San Francisco, August 1987.
bumps.dream.acr.ACR(p, n, alpha=0.05)[source]

Return critical value for test of single multivariate normal outlier using the Mahalanobis distance metric.

p is the number of independent variables, n is the number of samples, and alpha is the significance level cutoff (default=0.05).