A note on the waiting times between record observations
| Autor: | Paul T. Holmes, William E. Strawderman |
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| Rok vydání: | 1969 |
| Předmět: | |
| Zdroj: | Journal of Applied Probability. 6:711-714 |
| ISSN: | 1475-6072 0021-9002 |
| DOI: | 10.1017/s0021900200026772 |
| Popis: | Let X 1, X 2, X 3,··· be independent, identically distributed random variables with a continuous distribution function and let the sequence of indices {Vr } be defined as follows: and for r ≧ 1, V r is the trial on which the rth (upper) record observation occurs. {V r} will be an infinite sequence of random variables since the underlying distribution function of the X's is continuous. It is well known that the expected value of V r. is infinite for every r (see, for example, Feller [1], page 15). Also define and for r > 1 δr is the number of trials between the (r - l)th and the rth record. The distributions of the random variables Vr and δ r do not depend on the distribution of the original random variables. It can be shown (see Neuts [2], page 206 or Tata 1[4], page 26) that The following theorem is due to Neuts [2]. |
| Databáze: | OpenAIRE |
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