Table of Percentage Points of Pearson Curves, for Given √β 1 and β 2 , Expressed in Standard Measure

Johnson, N. L.; Nixon, Eric; Amos, D. E.; Pearson, E. S.

doi:10.2307/2333914

Cited by 8 publications

(3 citation statements)

References 6 publications

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“…Instead of computing from the density directly, we will make use of the tables produced by Johnson et al (1963). For this purpose, we need the following double entry interpolations.…”

Section: Pearson Type I Approximationmentioning

confidence: 99%

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On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts

Liang

Lee

Shao

2006

Journal of Applied Statistics

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This paper establishes a sampling theory for an inverted linear combination of two dependent F-variates. It is found that the random variable is approximately expressible in terms of a mixture of weighted beta distributions. Operational results, including rth-order raw moments and critical values of the density are subsequently obtained by using the Pearson Type I approximation technique. As a contribution to the probability theory, our findings extend Lee & Hu's (1996) recent investigation on the distribution of the linear compound of two independent F-variates. In terms of relevant applied works, our results refine Dickinson's (1973) inquiry on the distribution of the optimal combining weights estimates based on combining two independent rival forecasts, and provide a further advancement to the general case of combining three independent competing forecasts. Accordingly, our conclusions give a new perception of constructing the confidence intervals for the optimal combining weights estimates studied in the literature of the linear combination of forecasts.Combining weights, critical values, error-variance minimizing criterion, inverted F-variates, Pearson Type I approximation,

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“…Instead of computing from the density directly, we will make use of the tables produced by Johnson et al (1963). For this purpose, we need the following double entry interpolations.…”

Section: Pearson Type I Approximationmentioning

confidence: 99%

“…Owing to the complexity of the derived distribution, the fourth section presents several operational results, including rth-order raw moments and critical values of the density based on the Pearson Type I approximation technique (Johnson et al, 1963). The fifth section summarizes our findings and indicates future research directions.…”

Section: Introductionmentioning

confidence: 96%

On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts

Liang

Lee

Shao

2006

Journal of Applied Statistics

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“…Moreover, a method for computing specific Pearson percentiles is also described in Davis and Stephens (1983). However the problems of classification can not be solved on the basis of an estimation of percentiles only (Johnson et al, 1963;Pearson, 1954). These reviews being relatively condensed, we give a detailed description of the method for reader's convenience.…”

Section: Pearson Curves For the Approximation Of Statistical Distribumentioning

confidence: 99%

Classification of probability densities on the basis of Pearson’s curves with application to coronal heating simulations

Podladchikova

Lefebvre²,

Krasnoselskikh³

et al. 2003

Nonlin. Processes Geophys.

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Abstract. An important task for the problem of coronal heating is to produce reliable evaluation of the statistical properties of energy release and eruptive events such as microand nanoflares in the solar corona. Different types of distributions for the peak flux, peak count rate measurements, pixel intensities, total energy flux or emission measures increases or waiting times have appeared in the literature. This raises the question of a precise evaluation and classification of such distributions. For this purpose, we use the method proposed by K. Pearson at the beginning of the last century, based on the relationship between the first 4 moments of the distribution. Pearson's technique encompasses and classifies a broad range of distributions, including some of those which have appeared in the literature about coronal heating. This technique is successfully applied to simulated data from the model of Krasnoselskikh et al. (2002). It allows to provide successful fits to the empirical distributions of the dissipated energy, and to classify them as a function of model parameters such as dissipation mechanisms and threshold.

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Estimation of Travel Distance

Brimberg¹,

Walker²

2005

Encyclopedia of Statistical Sciences

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In this chapter we discuss the use of empirical distance functions in business models. The traditional role of distance functions has been to estimate travel distances or times in a given transportation system. We examine the properties of distance functions that make them useful in this role, and review popular ones such as the Euclidean norm, rectangular (or Manhattan) norm, and the more general weighted ℓ p norm and block norm. Statistical methods used to estimate the parameters of an empirical distance function from actual travel distance data are presented. This includes a review of the various goodness‐of‐fit criteria appearing in the literature, and a discussion of their error term distributions. The usefulness of empirical distance functions in modeling service systems of ever‐increasing size and complexity, and their growing relevance in operational and strategic decision processes, are also investigated. Future areas of research are identified in closing.

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Table of Percentage Points of Pearson Curves, for Given √β 1 and β 2 , Expressed in Standard Measure

Cited by 8 publications

References 6 publications

On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts

On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts

Classification of probability densities on the basis of Pearson’s curves with application to coronal heating simulations

Estimation of Travel Distance

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