A General Model of Random Variation

Shore, Haim

doi:10.1080/03610926.2013.784990

Cited by 5 publications

(6 citation statements)

References 11 publications

(25 reference statements)

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Section: Rmm Modeling Of Monotone Convex Ecological Relationshipsmentioning

confidence: 72%

“…This also shows in the small error (relative to the response). Approximated via RMM modeling, many other published models delivered similar patterns for the error plots (Shore,9,31 Benson-Karhi et al 11 ). Furthermore, attempts to use other commonly applied models as general modeling platforms failed to deliver comparable goodness of approximation.…”

Section: Rmm Approximation For Published Ecological Modelsmentioning

confidence: 72%

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Modeling and Monitoring Ecological Systems—A Statistical Process Control Approach

Shore

2013

Quality & Reliability Eng

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Statistical process control monitoring of nonlinear relationships (profiles) has been the subject of much research recently. While attention is primarily given to the statistical aspects of the monitoring techniques, little effort has been devoted to developing a general modeling approach that would introduce ‘uniformity of practice’ in modeling nonlinear profiles (analogously with the three‐sigma limits of Shewhart control charts). In this article, we use response modeling methodology (RMM) to demonstrate implementation of this approach to statistical process control monitoring of ecological relationships. Using 10 ecological models that have appeared in the literature, it is first shown that RMM models can replace (approximate) current ecological models with negligible loss in accuracy. Computer simulation is then used to demonstrate that estimated RMM models and estimated data generating ecological models achieve goodness‐of‐fit that is practically indistinguishable from one another. A regression‐adjusted control scheme, based on control charts for the predicted median and for residuals variation, is developed and demonstrated for three types of ‘out of control’ scenarios. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Rmm Modeling Of Monotone Convex Ecological Relationshipsmentioning

confidence: 72%

Section: Rmm Approximation For Published Ecological Modelsmentioning

confidence: 72%

Modeling and Monitoring Ecological Systems—A Statistical Process Control Approach

Shore

2013

Quality & Reliability Eng

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“…To examine further the validity of the “Random‐identity Paradigm”, as detailed earlier, we employ a third source in the form of a random sample of 27 theoretical distributions, used in Shore 12 . Details of this sample are given in Supplementary Material.…”

Section: How Random‐identity (Partial or Complete) Affects Shape Prop...mentioning

confidence: 99%

“…To examine further the validity of the "Random-identity Paradigm", as detailed earlier, we employ a third source in the form of a random sample of 27 theoretical distributions, used in Shore. 12 Details of this sample are given in Supplementary Material. We first delete from the set negatively-skewed distributions (we are reminded that only eight of the 126 surgery subcategories, as detailed in Shore, 1 had negative Sk estimates, all larger than −1, possibly reflecting sampling deviation from zero).…”

Section: Versus Skmentioning

confidence: 99%

A novel approach to modeling steady‐state process‐time with smooth transition from repetitive to semi‐repetitive to non‐repetitive (memoryless) processes

Shore

2023

Quality & Reliability Eng

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Defining properly the time distribution of a steady‐state process is crucial to its management. A common practice is to assume that process‐time is normally distributed for repetitive processes (process has constant work‐content), and exponentially for non‐repetitive processes (memoryless; no characteristic work‐content). This dichotomous distinction ignores the majority of processes, residing in between the two extreme scenarios, the semi‐repetitive ones. These processes own a characteristic duration time (as reflected in the mode), yet part of work‐content (“process identity”) randomly varies between cycles. In this paper, we develop a unified platform to model process‐time, comprising all three types of processes. The effects of work‐content instability on shape characteristics of process‐time distribution are studied, and process repetitiveness measure, possibly to be used to monitor work‐content instability, is defined. The generalized gamma distribution is employed to approximate the (unknown) distribution of process‐time sample mean, becoming exact for the two extreme scenarios (repetitive and non‐repetitive processes).

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“…For variations on the g ‐and‐ h approach, see Rayner & MacGillivray , Fischer et al , and the many references therein. For other transformation forms applied to g = φ , see Shore .…”

Section: The Menu: Four (Or Five) Main Familiesmentioning

confidence: 99%

On Families of Distributions with Shape Parameters

Jones

2014

Int Statistical Rev

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Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi-dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on R with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all-important location and scale parameters. One important and useful family is comprised of the 'skew-symmetric' distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call 'transformation of scale'-including two-piece distributions-and by probability integral transformation of nonuniform random variables. I also treat briefly the issues of multi-variate extension, of distributions on subsets of R and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal.

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A General Model of Random Variation

Cited by 5 publications

References 11 publications

Modeling and Monitoring Ecological Systems—A Statistical Process Control Approach

Modeling and Monitoring Ecological Systems—A Statistical Process Control Approach

A novel approach to modeling steady‐state process‐time with smooth transition from repetitive to semi‐repetitive to non‐repetitive (memoryless) processes

On Families of Distributions with Shape Parameters

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