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Two principal points of symmetric, strongly unimodal distributions

Author

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  • Tarpey, Thaddeus

Abstract

Examples illustrate that splitting a symmetric, unimodal distribution into two groups so as to minimize the sum of the within-group variances does not always occur at the mean. Strong unimodality is shown to be a sufficient condition for the optimal cutpoint to occur at the mean.

Suggested Citation

  • Tarpey, Thaddeus, 1994. "Two principal points of symmetric, strongly unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 253-257, July.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:4:p:253-257
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    Citations

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    Cited by:

    1. Yu, Feng, 2022. "Uniqueness of principal points with respect to p-order distance for a class of univariate continuous distribution," Statistics & Probability Letters, Elsevier, vol. 183(C).
    2. Jiang, Jia-Jian & He, Ping & Fang, Kai-Tai, 2015. "An interesting property of the arcsine distribution and its applications," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 88-95.
    3. Matsuura, Shun & Kurata, Hiroshi, 2011. "Principal points of a multivariate mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 213-224, February.
    4. Thaddeus Tarpey, 2007. "A parametric k-means algorithm," Computational Statistics, Springer, vol. 22(1), pages 71-89, April.
    5. Li, Luning & Flury, Bernard, 1995. "Uniqueness of principal points for univariate distributions," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 323-327, December.
    6. Thaddeus Tarpey, 1997. "Estimating principal points of univariate distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(5), pages 499-512.
    7. Yamamoto, Wataru & Shinozaki, Nobuo, 2000. "On uniqueness of two principal points for univariate location mixtures," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 33-42, January.
    8. Bali, Juan Lucas & Boente, Graciela, 2009. "Principal points and elliptical distributions from the multivariate setting to the functional case," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1858-1865, September.
    9. Santanu Chakraborty & Mrinal Kanti Roychowdhury & Josef Sifuentes, 2021. "High Precision Numerical Computation of Principal Points for Univariate Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 558-584, November.
    10. Yinan Li & Kai-Tai Fang & Ping He & Heng Peng, 2022. "Representative Points from a Mixture of Two Normal Distributions," Mathematics, MDPI, vol. 10(21), pages 1-28, October.
    11. Matsuura, Shun & Kurata, Hiroshi, 2010. "A principal subspace theorem for 2-principal points of general location mixtures of spherically symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1863-1869, December.

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