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Nagaraja, H. N.; Sen, Pali; Srivastava, R. C.

Some characterizations of geometric tail distributions based on record values. (English) Zbl 0666.62011

Stat. Hefte 30, No. 2, 147-155 (1989).
Let \(R_ j\) be the jth upper record value from an infinite sequence of independent identically distributed positive integer valued random variables. We show that their common distribution must have geometric tail if \(R_{j+k}-R_ j\) and \(R_ j\) are partially independent for some \(j\geq 1\) and \(k\geq 1\) or if \(E(R_{j+2}-R_{j+1}| R_ j)\) is a constant. Three versions of partial independence, each of which provides a characterization of the geometric tail are presented.

Cited in 7 Documents

MSC:

62E10 Characterization and structure theory of statistical distributions

Keywords:

geometric distribution; constant regression; upper record value; infinite sequence of independent identically distributed positive integer valued random variables; geometric tail; partial independence; characterization
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References:

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