The Distribution of the Record Position and its Applications |
| |
Authors: | Gunnar Blom Daniel Thorburn Theodore A Vessey |
| |
Institution: | 1. Department of Mathematical Statistics , Lund University , S-221 00 , Lund , Sweden;2. Department of Statistics , Stockholm University , S-106 91 , Stockholm , Sweden;3. Department of Mathematics , St. Olaf College , Northfield , MN , 55057 , USA |
| |
Abstract: | This is mainly an expository article on the positions of records in sequences of ordered elements. Such sequences are obtained, for example, when observing and ordering continuous iid random variables. In practice, records are of interest, for example, in meteorology and sports. A k-record is obtained when a new element is placed at position k counted from the top. The sequences of time points, when new k-records occur, are studied by elementary random walk methods. In the last section, it is shown that the time scale can be changed so that the time points of the k-records follow, approximately, a Poisson process. |
| |
Keywords: | Accelerated random walk Card file k-record Poisson process Random walk |
|
|