On the asymptotics of discrete order statistics. (English) Zbl 0987.62006
Summary: Let \(X_1,X_2, \dots, X_n\) be a sequence of independent, identically distributed positive integer random variables. We study the asymptotics of the likelihood that the sample maximum is achieved \(k\) times and in its spacing relative to the second highest value. Earlier and other results are discussed in this context. Also, some investigation is made when the sample is Markovian. Different results emerge in this case.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 62G30 | Order statistics; empirical distribution functions |
| 62G32 | Statistics of extreme values; tail inference |
References:
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