Tests of a simple multinomial hypothesis when the sample is not large

Conference · Wed Dec 31 23:00:00 EST 1980

OSTI ID:5498943

Atwood, C L

Outlying cells can be identified, based on the binomial distribution; the Bonferroni inequality then gives a conservative overall test. If instead, the Pearson chi-squared statistic is used, its distribution can be approximated as follows: condition on the counts in the first several cells, and approximate the conditional distribution as a shifted gamma distribution, matching the first two moments. Combine these approximate conditional distributions to obtain an approximate unconditional distribution. Generalized Chebyshev inequalities give bounds on the accuracy of the approximation; the fineness of the decomposition can be adjusted during the calculations to guarantee any desired accuracy. In examples, a good approximation is achieved by conditioning on those cells with the smallest probabilities.

• Research Organization: EG and G Idaho, Inc., Idaho Falls (USA)
• DOE Contract Number: AC07-76ID01570
• OSTI ID: 5498943
• Report Number(s): CONF-810842-3; ON: DE82005955
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics & Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL LOGIC
MATHEMATICS
MOMENTS METHOD
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
POLYNOMIALS
STATISTICS
TESTING