Generalized sooner waiting time problems in a sequence of trinary trials

Serkan Eryilmaz; Min Gong; Min Xie

doi:10.1016/j.spl.2016.04.003

Generalized sooner waiting time problems in a sequence of trinary trials

Serkan Eryilmaz^*, Min Gong, Min Xie

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

Abstract

Let {ξ_n, n≥1} be a sequence of independent trials with three possible outcomes 0, 1, 2 labeled as failure, success of type I and success of type II, respectively. Suppose that at each time a success of type I (type II) occurs in {ξ_n, n≥1} a random reward of type I (type II) is received. We obtain distributions of the number of trials until either the sum of consecutive rewards of type I is equal to or exceeds the level k₁ or the sum of consecutive rewards of type II is equal to or exceeds the level k₂ under two different schemes.

Original language	English
Pages (from-to)	70-78
Journal	Statistics and Probability Letters
Volume	115
DOIs	https://doi.org/10.1016/j.spl.2016.04.003
Publication status	Published - 1 Aug 2016

Research Keywords

Exact distribution
Sooner waiting time
Trinary trials
BERNOULLI TRIALS
FREQUENCY
SYSTEMS
QUOTAS
RUN

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title = "Generalized sooner waiting time problems in a sequence of trinary trials",

abstract = "Let {ξn, n≥1} be a sequence of independent trials with three possible outcomes 0, 1, 2 labeled as failure, success of type I and success of type II, respectively. Suppose that at each time a success of type I (type II) occurs in {ξn, n≥1} a random reward of type I (type II) is received. We obtain distributions of the number of trials until either the sum of consecutive rewards of type I is equal to or exceeds the level k1 or the sum of consecutive rewards of type II is equal to or exceeds the level k2 under two different schemes.",

keywords = "Exact distribution, Sooner waiting time, Trinary trials, BERNOULLI TRIALS, FREQUENCY, SYSTEMS, QUOTAS, RUN",

author = "Serkan Eryilmaz and Min Gong and Min Xie",

year = "2016",

month = aug,

day = "1",

doi = "10.1016/j.spl.2016.04.003",

language = "English",

volume = "115",

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journal = "Statistics and Probability Letters",

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TY - JOUR

T1 - Generalized sooner waiting time problems in a sequence of trinary trials

AU - Eryilmaz, Serkan

AU - Gong, Min

AU - Xie, Min

PY - 2016/8/1

Y1 - 2016/8/1

N2 - Let {ξn, n≥1} be a sequence of independent trials with three possible outcomes 0, 1, 2 labeled as failure, success of type I and success of type II, respectively. Suppose that at each time a success of type I (type II) occurs in {ξn, n≥1} a random reward of type I (type II) is received. We obtain distributions of the number of trials until either the sum of consecutive rewards of type I is equal to or exceeds the level k1 or the sum of consecutive rewards of type II is equal to or exceeds the level k2 under two different schemes.

AB - Let {ξn, n≥1} be a sequence of independent trials with three possible outcomes 0, 1, 2 labeled as failure, success of type I and success of type II, respectively. Suppose that at each time a success of type I (type II) occurs in {ξn, n≥1} a random reward of type I (type II) is received. We obtain distributions of the number of trials until either the sum of consecutive rewards of type I is equal to or exceeds the level k1 or the sum of consecutive rewards of type II is equal to or exceeds the level k2 under two different schemes.

KW - Exact distribution

KW - Sooner waiting time

KW - Trinary trials

KW - BERNOULLI TRIALS

KW - FREQUENCY

KW - SYSTEMS

KW - QUOTAS

KW - RUN

UR - http://www.scopus.com/inward/record.url?scp=84969509019&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84969509019&origin=recordpage

U2 - 10.1016/j.spl.2016.04.003

DO - 10.1016/j.spl.2016.04.003

M3 - RGC 21 - Publication in refereed journal

SN - 0167-7152

VL - 115

SP - 70

EP - 78

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Generalized sooner waiting time problems in a sequence of trinary trials

Abstract

Research Keywords

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