Abstract
Suppose that I1, I2, ⋯ is a sequence of independent Bernoulli random variables with E(In) = λ/(λ + n - 1), n = 1, 2, ⋯. If λ is a positive integer k, {In}n≥1 can be interpreted as a k-record process of a sequence of independent and identically distributed random variables with a common continuous distribution. When In-1I n = 1, we say that a consecutive k-record occurs at time n. It is known that the total number of consecutive k-records is Poisson distributed with mean k. In fact, for general λ > 0, ∑∞ n=2 In-1In is Poisson distributed with mean λ. In this paper, we want to find an optimal stopping time τλ which maximizes the probability of stopping at the last n such that I n-1In = 1. We prove that τλ is of threshold type, i.e. there exists a τλ ε ℕ such that τλ = min{n
| Original language | English |
|---|---|
| Pages (from-to) | 739-760 |
| Number of pages | 22 |
| Journal | Advances in Applied Probability |
| Volume | 42 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2010 Sep 1 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics
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Selecting the last consecutive record in a record process. / Hsiau, Shoou Ren.
In: Advances in Applied Probability, Vol. 42, No. 3, 01.09.2010, p. 739-760.Research output: Contribution to journal › Article
TY - JOUR
T1 - Selecting the last consecutive record in a record process
AU - Hsiau, Shoou Ren
PY - 2010/9/1
Y1 - 2010/9/1
N2 - Suppose that I1, I2, ⋯ is a sequence of independent Bernoulli random variables with E(In) = λ/(λ + n - 1), n = 1, 2, ⋯. If λ is a positive integer k, {In}n≥1 can be interpreted as a k-record process of a sequence of independent and identically distributed random variables with a common continuous distribution. When In-1I n = 1, we say that a consecutive k-record occurs at time n. It is known that the total number of consecutive k-records is Poisson distributed with mean k. In fact, for general λ > 0, ∑∞ n=2 In-1In is Poisson distributed with mean λ. In this paper, we want to find an optimal stopping time τλ which maximizes the probability of stopping at the last n such that I n-1In = 1. We prove that τλ is of threshold type, i.e. there exists a τλ ε ℕ such that τλ = min{n
AB - Suppose that I1, I2, ⋯ is a sequence of independent Bernoulli random variables with E(In) = λ/(λ + n - 1), n = 1, 2, ⋯. If λ is a positive integer k, {In}n≥1 can be interpreted as a k-record process of a sequence of independent and identically distributed random variables with a common continuous distribution. When In-1I n = 1, we say that a consecutive k-record occurs at time n. It is known that the total number of consecutive k-records is Poisson distributed with mean k. In fact, for general λ > 0, ∑∞ n=2 In-1In is Poisson distributed with mean λ. In this paper, we want to find an optimal stopping time τλ which maximizes the probability of stopping at the last n such that I n-1In = 1. We prove that τλ is of threshold type, i.e. there exists a τλ ε ℕ such that τλ = min{n
UR - http://www.scopus.com/inward/record.url?scp=78650951871&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78650951871&partnerID=8YFLogxK
U2 - 10.1239/aap/1282924061
DO - 10.1239/aap/1282924061
M3 - Article
AN - SCOPUS:78650951871
VL - 42
SP - 739
EP - 760
JO - Advances in Applied Probability
JF - Advances in Applied Probability
SN - 0001-8678
IS - 3
ER -