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Effects of Heterogeneity of Variance on the Probability of Correctly Identifying the Best Normal Population

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Abstract

This study examines the effects of heterogeneity of variance on the probability of making the correct selection when using the means procedure for selecting the population with the largest mean from a set of independent normal populations. The study is conducted by using Monte Carlo simulation techniques for 3, 4, and 5 normal populations as an application of pattern recognition and classification. The population means and standard deviations are assumed to be equally-spaced. Two types of heterogeneity of variane are considered: (1) associating larger variances with larger means, and (2) associating smaller variances with larger means.

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References

  1. Bechhofer, R.E. A single sample multiple decision procedure for randking means of normal populations with known variances. The Annals of Mathematical Statistics , 1954 25, 16–39.

    Google Scholar 

  2. Carroll, R.J. & Cupta, S.S. On the probabilities of rankings of k populations with applications. Journal of Statistical Computation and Simulation 1977, 5. 145–157.

    Article  MATH  Google Scholar 

  3. Cibbons, J P. Olkin, I. & Sobel, M. Selecting and ordering Populations: A new Statistical Methodology. New York Wiley, 1977.

    Google Scholar 

  4. Gupta, S.S. Selection and ranking procedures: A brief introduction. Communications in Statistics Theory and Methods. 1977, A6. 933–1001.

    Google Scholar 

  5. Gupta, S.S. & Singh, A.K. On rules based on sample medians for selection of the largest location parameter. Communications in Statistics - Theory and Methods. 1980 A9. 1277–1298.

    Article  MathSciNet  Google Scholar 

  6. Hall, W.J. The most economical character of some Bechhofer and Sobel decision rules. The Annals of Mathematical Statistics. 1959, 30. 964–969.

    Article  MATH  Google Scholar 

  7. Kleijnen, J.P.C. Statistical techniques in simulation. New York Marcel Dekker, 1975

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  8. Knuth, D.E. The art of computer programming, Vol.2. Seminumerical Algorithms. Reading PA: Addison-Wesley, 1969.

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© 1988 Plenum Press, New York

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Zaher, A.M., Azmi, Z.A. (1988). Effects of Heterogeneity of Variance on the Probability of Correctly Identifying the Best Normal Population. In: Cantoni, V., Di Gesù, V., Levialdi, S. (eds) Image Analysis and Processing II. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1007-5_32

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  • DOI: https://doi.org/10.1007/978-1-4613-1007-5_32

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8289-1

  • Online ISBN: 978-1-4613-1007-5

  • eBook Packages: Springer Book Archive

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