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Statistica Sinica 7(1997), 893-906


Masaaki Sibuya and Kazuo Nishimura

Keio University and Komazawa University

Abstract: For analyzing record statistics from a sequence of non-i.i.d. random variables, a model with one or two parameters, controlling the occurrences of record-breakings, is proposed. Under the model, the number of record-breakings within n steps has a probability function including the Stirling-Carlitz polynomial of the first kind. Its expected number is still O(logn) and saturates in the long run. Waiting time to the sth occurrence also has a probability function of similar form. Under this model, methods for predicting future record-breakings are proposed, and applied to some practical data sets of weather and sports.

Key words and phrases: Nevzorov model, random walk, record value theory, Stirling-Carlitz polynomial, Stirling family of discrete distributions.

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