Exact Lower Moments of Order Statistics in Small Samples from a Normal Distribution

Jones, Howard L.

doi:10.1214/aoms/1177730253

Cited by 33 publications

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“…We say double integration because G(x) is itself an indefinite integral. (The one exception, where an analytic result is possible, is the special case of n = 2 for the normal distribution; see Jones [9]). Even the expected value E(Lp)) and the variance V ( L p ) ) cannot be expressed in analytic form.…”

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confidence: 99%

Safety stock reduction by order splitting

Kelle

Silver

1990

Naval Research Logistics

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In this article we consider an item for which a continuous review, reorder point, order quantity inventory control system is used. The amount of safety stock required depends upon, among other factors, the average value and variability of the length of the replenishment lead time. One way to reduce these quantities is to split orders among two or more vendors. In this article the random lead times are assumed to have Weibull distributions. This permits the development of analytic expressions for the reduction in the expected value and variability of total demand until the critical first (earliest) delivery received from a vendor. An expression is also obtained for the reorder point that provides a given probability of no stockout prior to the first delivery. Lower bounds are given on the order quantity so as to ensure that the probability of a stockout before any one of the later (second, third, etc.) deliveries is sufficiently small to be considered negligible. The analytic and tabular results can be used to estimate the benefits (reduced carrying costs and/or increased service level) of order splitting.

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confidence: 99%

Safety stock reduction by order splitting

Kelle

Silver

1990

Naval Research Logistics

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“…Table 1 contains the coefficient matrix X from the Taylor series expansion p = (1/6)1 + Xy. For small values of r, expressions are available in closed form for such constants as OJ:r and Ojj:r (see Jones (1948) and Godwin (1949)).…”

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confidence: 99%

Normal Order Statistics as Permutation Probability Models

Dansie

1986

Applied Statistics

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“…2, d . t he rBr~ren cc for t he C3SC of the rectangular universe' is Wilks [6]; for t h~ normal universe, Jones [9] . T ile values for the rectan gular universe are computed by finding t he momen ts of ya for the square universe and t hen adjusting by the location and scale factors desrribed in 8cctiou 3.…”

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confidence: 99%

Properties of certain statistics involving the closest pair in a sample of three observations

Lieblein¹

1952

J. RES. NATL. BUR. STAN.

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Triplicate readings are of wide occurrence in experimen tal work. Occasio nally, however, only the closest pair of a triad is used, and the outlyi ng high or low one discarded as evi dencing so me gross error. The present paper presen ts a mathematical investigat ion leadi ng to precise determination of so me of the biases that result from such selection . This project was suggested by certain experiments involving random sampling numbers a nd a nalysis of publishe d chemical determinatio ns. The theoretical findin gs agree closely with t he empirical resu lts and imply that selected pairs not o nly te nd to overestimate cons iderably the precision of the experimental procedure, but also res ult in less accurate determinations.

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Exact Lower Moments of Order Statistics in Small Samples from a Normal Distribution

Cited by 33 publications

References 0 publications

Safety stock reduction by order splitting

Safety stock reduction by order splitting

Normal Order Statistics as Permutation Probability Models

Properties of certain statistics involving the closest pair in a sample of three observations

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