Browse > Article
http://dx.doi.org/10.7465/jkdi.2012.23.2.411

Simulation study on the estimation of multinomial proportions  

Kim, Dae-Hak (Department of Mathematics, Catholic University of Daegu)
Publication Information
Journal of the Korean Data and Information Science Society / v.23, no.2, 2012 , pp. 411-417 More about this Journal
Abstract
In this paper, we consider the estimation of multinomial proportions. Multinomial distribution is the most important multivaritate distribution. Estimation of multinomial parameters for multinomial distribution is widely applicable to many practical research areas including genetics. We investigated the properties of several frequency substitution estimates and derived the maximum likelihood estimate of multinomial proportions of Hardy Weinberg proportions. Phenotype and genotype frequencies of allele are used to the estimation of multinomial proportions. These estimates are then analyzed via numerical data. Small sample Monte Carlo simulation is conducted to compare considered estimates of multinomial proportions.
Keywords
Hardy Weinberg proportions; Monte Carlo simulation; multinomial distribution; phenotype allele; proportion estimation;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Kang, C. (2003). Bootstrap method for the estimation of negative binomial parameter k. Journal of the Korean Data Analysis Society, 5, 519-525.
2 Lee, J. C. and Lee, C. S. (2012). An approximate maximum likelihood estimator in a weighted exponential distribution. Journal of the Korean Data & Information Science Society, 23, 219-225.   DOI   ScienceOn
3 Lee, J. W., Kim, H. Lee, H. J. (2006). A simulation study on gene-environment interaction. Journal of the Korean Data Analysis Society, 8, 927-938.
4 Mosteller, F. (1968). Association and estimation in contingency tables. Journal of the American Statistical Association, 63, 1-28.   DOI   ScienceOn
5 Park, C. G. (2011). Estimation of error variance in nonparametric regression under a nite sample using ridge regression. Journal of the Korean Data & Information Science Society, 22, 1223-1232.
6 Park, H. I. and Kim, J. S. (2011). An estimation of the treatment e ect for the right censored data. Journal of the Korean Data & Information Science Society, 22, 537-547.
7 Pearson, K. (1903). Mathematical contributions to the theory of evolution, XI. On the influence of natural selection on the variability and correlation of organs. Philosophical Transactions of the Royal Society of London A, 1-66.
8 Shi, Z., Lee, J. H, Lee, Y. S., Oh, D. Y. and Yeo, J. S. (2011). Analysis of genetic diversity and distances in Asian cattle breeds using microsatellite markers. Journal of the Korean Data & Information Science Society, 21, 795-802.
9 Stern, C. (1943). The Hardy-Weinberg law. Science, 97, 137-138.   DOI
10 Bickel, P. J. and Doksum, K. A. (1977). Mathematical statistics: Basic ideas and selected topics, Holden-Day, Inc.
11 Cho, J. S. (2006). Multiple comparison of the proportions for negative binomial populations using fractional Bayes factor. Journal of the Korean Data Analysis Society, 8, 1361-1368.
12 Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics, reprinted in contributions to mathematical statistics, John Wiley & Sons, New York.
13 Ford, E. B. (1971). Ecological genetics, Chapman and Hall, London.