• Corpus ID: 9665557

THE EXACT ASYMPTOTIC DISTRIBUTION FUNCTION OF WATSON ’ S UN 2 FOR TESTING GOODNESS-OFFIT WITH CIRCULAR DISCRETE DATA *

@inproceedings{Giles2006THEEA,
  title={THE EXACT ASYMPTOTIC DISTRIBUTION FUNCTION OF WATSON ’ S UN 2 FOR TESTING GOODNESS-OFFIT WITH CIRCULAR DISCRETE DATA *},
  author={David E. A. Giles},
  year={2006}
}
* We are grateful to Sophie Hesling for her assistance with data collection. Abstract We show that the full asymptotic distribution for Watson's 2 N U statistic, modified for discrete data, can be computed by standard methods. Previous approximate percentiles for the uniform multinomial case are found to be accurate. More extensive percentiles are presented for this distribution, and for the distribution associated with " Benford's Law " . 

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References

SHOWING 1-10 OF 22 REFERENCES

Watson's UN2 statistic for a discrete distribution

SUMMARY A general method is given for obtaining approximate percentiles of the asymptotic distribution of Watson's UN for testing goodness of fit to a completely specified discrete distribution. The

The distribution of the goodness-of-fit statistic U2N. I

In Part 1 (Stephens, 1963) were given the moments, and some small-sample results, of the distribution of UN. This is a goodness-of-fit statistic introduced by Watson (1961, 1962), and tests the null

The goodness-of-fit statistic VN: distribution and significance points

1.1. Kuiper (1960) has proposed VN, an adaptation of the Kolmogorov statistic, to test the null hypothesis that a random sample of size N comes from a population with given continuous distribution

Distribution theory for tests based on the sample distribution function

Computing the distribution of quadratic forms in normal variables

In this paper exact and approximate methods are given for computing the distribution of quadratic forms in normal variables. In statistical applications the interest centres in general, for a

Detecting Fraud in Data Sets Using Benford's Law

TLDR
A statistical detection method developed by Nigrini to test whether or not a particular data set follows Benford's Law is discussed; the purpose of this method is to detect fraud in data sets such as tax data.

The distribution of a linear combination of 2 random variables

pr(Q<c). (2) The algorithm is based on the method of Davis (1973) involving the numerical inversion of the characteristic function. It will yield results for most linear combinations that are likely

Theory of analogous force on number sets

Benford's law and naturally occurring prices in certain ebaY auctions

We show that certain winning bids for certain ebaY auctions obey Benford's Law. One implication of this is that it is unlikely that these bids are subjected to collusion among bidders, or ‘shilling’

Numerical inversion of a characteristic function

SUMMARY A method is described for finding a bound on the error when a version of the usual characteristic function inversion formula is evaluated by numerical integration. The method is applied to