StatsInvUSquaredCDF

StatsInvUSquaredCDF (cdf, n, m, method, useTable)

The StatsInvUSquaredCDF function returns the inverse of Watson's U² cumulative distribution function integer sample sizes n and 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. 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.

The inverse is obtained from precomputed tables of Watson's U² (see StatsUSquaredCDF).

note

Table values are different from computed values. These values use more conservative criteria than computed values. Table values are more consistent with published values because the U2 distribution is a highly irregular function with multiple steps of arbitrary sizes. The standard for published tables provides the X value of the next vertical transition to the one on which the specified P is found. See StatsInvFriedmanCDF.

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, StatsUSquaredCDF