Peakedness and Peakedness Ordering

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  • Date/Time:
    • Thursday April 21, 2011
      12:00 pm - 1:00 pm
  • Location: IC 115
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Summary Sentence: Peakedness and Peakedness Ordering

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TITLE:  Peakedness and Peakedness Ordering

SPEAKER:  Hammou El Barmi

ABSTRACT:

The peakedness of a random variable (RV) X about a point a is defined by Pa(x)= P (|X − a|≤ x),x ≥ 0. A RV X is said to be less peaked about a than a RV Y about b, denoted by X ≤pkd(a,b) Y , if P (|X − a|≤ x) ≤ P (|Y − b|≤ x) for all x ≥ 0, i.e., |X − a| is stochastically larger than |Y − b|. These generalize the original definitions of Birnbaum (1948) who considered the cases where X and Y were symmetric about a and b, respectively. Statistical inferences about the distribution functions of continuous X and Y under peakedness ordering in the symmetric case have been treated in the literature. Rojo et al. (2007) provided estimators of the distributions in the general case and analyzed their properties. We show that these estimators could have poor asymptotic properties relative to those of the empiricals. We provide improved estimators of the DFs, show that they are consistent, derive the weak convergence of the estimators, compare them with the empirical estimators, and provide formulas for statistical inferences.

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Status
  • Created By: Anita Race
  • Workflow Status: Published
  • Created On: Apr 12, 2011 - 9:38am
  • Last Updated: Oct 7, 2016 - 9:54pm