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A New Proof for Monotone Likelihood Ratio for the Sum of Independent Bernoulli Random Variables

Published online by Cambridge University Press:  01 January 2025

Huynh Huynh
Huynh Huynh*
Affiliation:
University of South Carolina
*
Requests for reprints should be addressed to Huynh Huynh, College of Education, University of South Carolina, Columbia, SC 29208.
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Abstract

By use of an inequality of Marcus and Lopes for elementary symmetric functions, a new proof is presented for the following result by Ghurye and Wallace: Given that the independent random variables Xj are Bernoulli with success probability pj (θ) strictly between 0 and 1 and nondecreasing in θ, the sum ΣXj has monotone likelihood ratio.

Keywords

Bernoullibinary random variableselementary symmetric functionsmonotone likelihood ratio
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 1 , March 1994 , pp. 77 - 79
Copyright
Copyright © 1994 The Psychometric Society

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References

Ferguson, T. S. (1967). Mathematical statistics: A decision-theoretic approach, New York: Academic Press.Google Scholar
Fischer, G. H. (1974). Einfuhrung in die theorie psychologisher tests [Introduction to the theory of psychological tests], Bern: Huber.Google Scholar
Ghurye, S. G., Wallace, D. L. (1959). A convolutive class of monotone likelihood ratio families. Annals of Mathematical Statistics, 30, 1158–1164.CrossRefGoogle Scholar
Grayson, D. A. (1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 383–392.CrossRefGoogle Scholar
Gustafsson, J. E. (1980). A solution of the conditional estimation problem for long tests in the Rasch model for dichotomous items. Educational and Psychological Measurement, 40, 377–385.CrossRefGoogle Scholar
Hambleton, R. K., Swaminathan, H. (1985). Item response theory, Boston: Kluwer Academic Publisher Group.CrossRefGoogle Scholar
Huynh, H. (1976). Statistical consideration of mastery scores. Psychometrika, 41, 65–78.CrossRefGoogle Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading, Mass: Addison-Wesley.Google Scholar
Marcus, M., Lopes, L. (1957). Inequalities for symmetric functions and Hermitian matrices. Canadian Journal of Mathematics, 9, 305–312.CrossRefGoogle Scholar
Marshall, A. W., Olkin, I. (1979). Inequalities: Theory of majorization and its applications, New York: Academic Press.Google Scholar