1. Peakedness and peakedness ordering
- Author
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El Barmi, Hammou and Mukerjee, Hari
- Subjects
- *
RANDOM variables , *STOCHASTIC orders , *GENERALIZATION , *DISTRIBUTION (Probability theory) , *PARAMETER estimation , *EMPIRICAL research , *MATHEMATICAL statistics , *STOCHASTIC convergence - Abstract
Abstract: The peakedness of a random variable (RV) about a point is defined by . A RV is said to be less peaked about than a RV about , denoted by , if for all , i.e., is stochastically larger than . These generalize the original definitions of Birnbaum (1948) who considered the cases where and were symmetric about and , respectively. Statistical inferences about the distribution functions of continuous and 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. An example is also used to illustrate our theoretical results. [Copyright &y& Elsevier]
- Published
- 2012
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