Abstract
Distributional equations of the form [image omitted] are studied, where X and Y are neighboring generalized order statistics based on distribution function F, and V is a power function or Pareto distributed random variable, independent of Y. Characterizations of distributions via random contraction and random dilation are stated involving three conditions, namely, the distributional equation, the form of F and the distribution of V, where each two assertions imply the third. Recent results for the particular submodels of order statistics and record values are contained and also extended.
Original language | English |
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Pages (from-to) | 2185-2201 |
Number of pages | 17 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 37 |
Issue number | 14 |
DOIs | |
Publication status | Published - 1 Jan 2008 |
Externally published | Yes |
Keywords
- Characterizations of distributions
- Distributional equation
- Generalized order statistics
- Mellin transform
- Pareto distribution
- Power function distribution
- Weibull distribution