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Lower and upper bounds on the variances of spacings

Author

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  • Paweł Marcin Kozyra

    (Polish Academy of Sciences)

  • Tomasz Rychlik

    (Polish Academy of Sciences)

Abstract

For classic i.i.d. samples with an arbitrary nondegenerate and finite variance distribution, Papadatos (1995, Annals of the Institute of Statistical Mathematics, 47, 185–193) presented sharp lower and upper bounds on the variances of order statistics, expressed in population variance units. We provide here analogous results for spacings. Also, we describe the parent distributions which attain the bounds.

Suggested Citation

  • Paweł Marcin Kozyra & Tomasz Rychlik, 2017. "Lower and upper bounds on the variances of spacings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 417-428, April.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:2:d:10.1007_s10463-015-0545-6
    DOI: 10.1007/s10463-015-0545-6
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    References listed on IDEAS

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    1. Nickos Papadatos, 1995. "Maximum variance of order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 185-193, January.
    2. Lin, G. D. & Huang, J. S., 1989. "Variances of sample medians," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 143-146, June.
    3. Agnieszka Goroncy & Tomasz Rychlik, 2015. "Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 175-204, February.
    4. Danielak, Katarzyna & Rychlik, Tomasz, 2003. "Sharp bounds for expectations of spacings from DDA and DFRA families," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 303-316, December.
    5. Nickos Papadatos, 1997. "A Note on Maximum Variance of Order Statistics from Symmetric Populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 117-121, March.
    Full references (including those not matched with items on IDEAS)

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