Limit theorems for runs based on `small spacings' (Q618005)
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scientific article; zbMATH DE number 5836633
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limit theorems for runs based on `small spacings' |
scientific article; zbMATH DE number 5836633 |
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Limit theorems for runs based on `small spacings' (English)
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14 January 2011
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The following type of runs was proposed by Erylmaz and Stepanov (2008): a sequence of spacings forms a run if the lengths of these spacings do not exceed \(\epsilon > 0\). Asymptotic properties of these spacings were investigated and a statistical test proposed by them. In the present paper, the research on these runs is continued; limit theorems are derived for the total number of runs and for the longest run. A procedure based on these runs is proposed to test for the uniformity or exponentiality of the underlying distribution.
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