Journal ArticleDOI
An extension and implications of the inspection paradox
TLDR
In this paper, the authors generalize the inspection paradox, show a stochastic ordering of X1, XN, and then interpret and consider the ramifications of this stochastically ordering.About:
This article is published in Statistics & Probability Letters.The article was published on 1988-03-01. It has received 5 citations till now. The article focuses on the topics: Stochastic ordering & Constant (mathematics).read more
Citations
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Journal ArticleDOI
Continuity theorems for the M/M/1/n queueing system
TL;DR: Continuity theorems are established for the number of losses during a busy period of the M/M/1/n queueing system where the service time probability distribution is approximated by that exponential distribution.
Journal ArticleDOI
The inspection paradox with random time
TL;DR: In this paper, the renewal function and the expected length of the interarrival time of a control chart that contains some fixed time t were derived for a continuous NBU (NWU) distribution function.
Journal ArticleDOI
On a renewal process average
TL;DR: In this article, a simple representation of the expectation of a renewal process mean with random time is obtained, which leads to a renewal theoretic interpretation of certain premium calculation principles, and a simple interpretation of the renewal process can be found.
Journal ArticleDOI
Thickened renewal processes
Ron Doney,George L. O'Brien +1 more
TL;DR: In this article, the lifetime distribution function has the form F ( x ) = cx α (1 + λx + o (x )) near 0+ and the asymptotic conditional distribution as n → ∞ of { nt i, i ⩾ 0}, given that t n ⩽ 1, is that of a renewal process with a gamma lifetime distribution depending only on α.
Journal ArticleDOI
Continuity theorems for the $M/M/1/n$ queueing system
TL;DR: In this paper, continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queueing system, where the service time probability distribution, slightly different in a certain sense from the exponential distribution, is approximated by that exponential distribution.
References
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Unbiased Estimation in Fixed Cost Sequential Sampling Schemes
TL;DR: In this paper, fixed cost sequential sampling schemes are introduced, where units are observed sequentially according to a given sampling method until the total cost reaches a preassigned value; it is assumed that the cost of examining each unit is unknown in advance, and the notion of sufficiency in sampling can be used to construct unbiased estimators of population parameters under these schemes.