Name
Abstract | ||
|---|---|---|
We study the distribution of the number n;r of r consecutive records in a sequence of n independent and identically distributed random variables from a common continuous distribution, or equivalently, in a random permutation ofn elements. We show that the asymptotic distribution of n;r is Poisson for r = 1; 2 and non-Poisson for r 3. Precise asymptotic results are derived for four probability distances of the associated approximations: Fortet-Mourier, total variation, Kolmogorov, and point metric. In particular, the distributions of n;r have the specic property that the last three distances are asymptotically of the same behaviors for r 2. We also provide interesting combinatorial bijections for n;2 and compute explicitly the limiting law for n;3 in terms of Kummer's conuent hypergeometric functions. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1002/1098-2418(200010/12)17:3/4<169::AID-RSA1>3.0.CO;2-K | Random Struct. Algorithms |
Keywords | Field | DocType |
poisson approximations,point metric,consecutive records,dierential,kolmogorov distance,consecutive record,fortet-mourier distance,total variation distance,differential equation,asymptotic distribution,hypergeometric function,random permutation,random variable,limit laws,independent and identically distributed,total variation | Total variation,Hypergeometric function,Discrete mathematics,Combinatorics,Random permutation,Bijection, injection and surjection,Independent and identically distributed random variables,Poisson distribution,Mathematics,Asymptotic distribution,Frobenius method | Journal |
Volume | Issue | ISSN |
17 | 3-4 | 1042-9832 |
Citations | PageRank | References |
2 | 0.40 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hua-Huai Chern | 1 | 78 | 7.25 |
| Hsien-Kuei Hwang | 2 | 365 | 38.02 |
| Y.-N. Yeh | 3 | 253 | 44.47 |