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New estimators of distribution functions

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  • A. K. Md. Ehsanes Saleh
  • Amal Ghania

Abstract

This article considers the estimation of a distribution function FX(x) based on a random sample X1, X2, …, Xn when the sample is suspected to come from a close-by distribution F0(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F0(x). As a by-product similar estimators are proposed for population quantiles.

Suggested Citation

  • A. K. Md. Ehsanes Saleh & Amal Ghania, 2016. "New estimators of distribution functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(11), pages 3145-3157, June.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:11:p:3145-3157
    DOI: 10.1080/03610926.2014.897138
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