StatsUSquaredCDF

StatsUSquaredCDF (u2, n, m, method, useTable)

The StatsUSquaredCDF function returns the cumulative distribution function for Watson's U² with parameters u2 (U² statistic) and integer sample sizes n and m. The calculation is computationally intensive, on the order of binomial(n +m, m ). Use a nonzero value for useTable to search a built-in table of values. If n and m cannot be found in the table, it will proceed according to method :

method	What It Does
0	Exact computation using Burr algorithm (could be slow).
1	Tiku approximation using chi-squared.
2	Use built-in table only and return a NaN if not in table.

For large n and m, consider using the Tiku approximation. To abort execution, press the User Abort Key Combinations.

Precomputed tables, using the algorithm described by Burr, contain these values:

n	m
4	4-30
5	5-30
6	6-30
7	7-30
8	8-26
9	9-22
10	10-18
11	11-16
12	12-14
13	13

Because n and m are interchangeable, n should always be the smaller value. For n>8 the upper limit in the table matched the maximum that can be computed using the Burr algorithm. There is no point in using method 0 with m values exceeding these limits.

References

Burr, E.J., Small sample distributions of the two sample Cramer-von Mises' W² and Watson's U², Ann. Mah. Stat. Assoc., 64, 1091-1098, 1964.

Tiku, M.L., Chi-square approximations for the distributions of goodness-of-fit statistics, Biometrica, 52, 630-633, 1965.

See Also

Statistical Analysis, StatsWatsonUSquaredTest, StatsInvUSquaredCDF