Projection method for moment bounds on order statistics from restricted families. II: Independent case. (English) Zbl 0906.62050
Summary: The method of projection, proposed in Part I, ibid. 57, No. 1, 156-174, Art. No. 0027 (1996; Zbl 0863.62045), is applied to derive sharp moment bounds for the expectations of order statistics based on independent samples from restricted families of distributions. Three families are considered: life distributions with decreasing failure density, decreasing failure rate, and symmetric unimodal ones. The respective bounds are also numerically compared with those for general populations in both the dependent and independent cases. \(\copyright\) Academic Press.
MSC:
| 62G30 | Order statistics; empirical distribution functions |
| 62E10 | Characterization and structure theory of statistical distributions |
| 62E15 | Exact distribution theory in statistics |
Keywords:
independent; identically distributed random variables; decreasing failure rates; symmetric unimodal distribution; convex cone; Bernstein polynomial; variation diminishing propertyCitations:
Zbl 0863.62045References:
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