Author:
Holmes Paul T.,Strawderman William E.
Abstract
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].
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
10 articles.
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