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Topic: Edgeworth series

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	Edgeworth series - Wikipédia
		The Edgeworth series or Gram-Charlier A series, named in honor of Francis Ysidro Edgeworth, are series that approximate a probability distribution in terms of its cumulants.
		The key idea of these expansions is to write the characteristic function of the distribution whose probability density function is F to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover F through the inverse Fourier transform.
		Edgeworth developed a similar expansion as an improvement to the central limit theorem.
	su.wikipedia.org /wiki/Edgeworth_series (473 words)

	Francis Ysidro Edgeworth - Wikipedia, the free encyclopedia
		Edgeworth was a highly influential figure in the development of neo-classical economics.
		He developed utility theory introducing the indifference curve and the famous Edgeworth box which is now familiar to undergraduates of microeconomics.
		As a self-taught mathematical statistician he is remembered by the eponymous Edgeworth series.
	en.wikipedia.org /wiki/Francis_Edgeworth (408 words)

	Francis Ysidro Edgeworth
		Edgeworth's "range of final settlements" was later resurrected by Martin Shubik (1959) as the game-theoretic concept of "the core".
		Edgeworth also articulated what eventually became known as "Edgeworth's conjecture", namely that as the number of agents in an economy increase, the degree of indeterminacy is reduced.
		Edgeworth also set the utilitarian foundations for highly progressive taxation, arguing that the optimal distribution of taxes should be such that "the marginal disutility incurred by each taxpayer should be the same" (Edgeworth, 1897).
	cepa.newschool.edu /het/profiles/edgew.htm (3799 words)

	Edgeworth (Site not responding. Last check: 2007-10-08)
		Richard Lovell Edgeworth had an estate at Edgeworthstown, northwest of Dublin, and it was on this estate that Edgeworth was born.
		Edgeworth published Methods of Statistics in 1885 which presented an exposition of the application and interpretation of significance tests for the comparison of means.
		Edgeworth's work was to influence Pearson although bad feeling developed between the two and later Pearson was to deny Edgeworth's influence.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Edgeworth.html (1049 words)

	Edgeworth's "Indeterminacy of Contract"
		Edgeworth's interest in the process of barter exchange was sparked by a rather unsatisfactory discussion of the matter in William Stanley Jevons's Theory of Political Economy (1871).
		Edgeworth's principal endeavor was to demonstrate that bilateral barter exchange was not determinate, i.e.
		Edgeworth challenged Jevons's assertion of determinacy of barter exchange by showing that "Jevons's conditions" that (1) indifference curves are tangent at the solution trade and (2) that the solution trade is mutually beneficial, will yield a set of solutions represented by all the points on the region of final settlements.
	homepage.newschool.edu /~het/essays/edgew/edgecore.htm (4509 words)

	Asymptotic analysis - Wikipedia, the free encyclopedia
		The asymptotic point of view is basic in computer science, where the question is typically how to describe the resource implication of scaling-up the size of a computational problem, beyond the 'toy' level.
		An asymptotic expansion of a function f(x) is in practice an expression of that function in terms of an infinite series, the partial sums of which do not (necessarily have to) converge; but such that taking any initial partial sum provides an asymptotic formula for f.
		Asymptotic expansions typically arise in the approximation of certain integrals (saddle-point method, method of steepest descent) or in the approximation of probability distributions (Edgeworth series).
	www.wikipedia.org /wiki/Asymptotic (353 words)

	Abstracts of Papers by John Kolassa
		I demonstrate that the classical Edgeworth series provides an asymptotic expansion for the cumulative distribution function of a lattice random variable if the cumulants in this series are adjusted using Sheppard's corrections, and the series is evaluated at midpoints of the intervals between lattice points.
		In this case, the multivariate cumulants must be adjusted by the multivariate version of Sheppard's corrections, and the series must be evaluated at the midpoints of hypercubes whose vertices are lattice points.
		In light of standard Edgeworth series results for random variables confined to a lattice, this result is counterintuitive.
	www.stat.rutgers.edu /~kolassa/abs.html (2822 words)

	Edgeworth Expansions For Spectral Mean Estimates With Applications To Whittle Estimates - JANAS (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		We prove that the distributions of spectral mean estimates from linear processes admit Edgeworth expansions.
		As a consequence, Edgeworth expansions are valid for Whittle estimates.
		Edgeworth expansions for spectral mean estimates with applications to Whittle estimates.
	citeseer.ist.psu.edu /janas93edgeworth.html (403 words)

	Cash Co Tand
		Edgeworth, a Londoner, came to Melbourne in 1969 for the wedding of his brother Ron to Judith Durham (formerly of 'The Seekers').
		Edgeworth was surprised upon his arrival in Australia that there was no local historical drama on television.
		When filming of the first series was completed in January 1975, and before the decision was made to go ahead with a second batch of 13 episodes, Serge Lazareff decided to quit the show.
	www.classicaustraliantv.com /CashCoTandarra.htm (3533 words)

	Pickens County Herald Online (Site not responding. Last check: 2007-10-08)
		The winner of the best-of-three series that begins Friday, May 8, advances to the state finals.
		Edgeworth dusted the first eleven batters he faced and finished a seven-inning, 14K beauty, allowing just four hits and walking one.
		Edgeworth stayed strong even after Red Level plated two fifth inning runs to take a 2-1 lead.
	theherald.pickens.net /sports/5504_2.htm (533 words)

	Cumulant - Wikipédia
		is the nth coefficient in the power series representation of the logarithm of the moment-generating function.
		They were first called cumulants in a 1931 paper, The derivation of the pattern formulae of two-way partitions from those of simpler patterns, Proceedings of the London Mathematical Society, Series 2, v.
		All of the difficulties of the "problem of cumulants" are absent when one works "formally".
	su.wikipedia.org /wiki/Cumulant (1053 words)

	[No title]
		The resulting truncated series may be viewed as the normal probability density function multiplied by a polynomial that accounts for the effects of departure from normality.
		Although the series are equivalent, for computational purposes the Gram-Charlier series seems to perform better than the Edgeworth series (Johnson et al., 1994).
		Although the Gram-Charlier (and Edgeworth) expansion allows for additional flexibility over the normal probability density function because it introduces the skewness and kurtosis of the empirical distribution as parameters, this expansion has the drawback of yielding negative values for certain skewness-kurtosis parameters because it is a polynomial approximation.
	www.fintools.com /docs/GramCharlier.doc (976 words)

	Edgeworth series -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		/4) at infinity (Cramér 1957).] When it does not converge, the series is also not a true (Click link for more info and facts about asymptotic expansion) asymptotic expansion, because it is not possible to estimate the error of the expansion.
		Edgeworth developed a similar expansion as an improvement to the (Click link for more info and facts about central limit theorem) central limit theorem.
		The advantage of the Edgeworth series is that the error is controlled, so that it is a true (Click link for more info and facts about asymptotic expansion) asymptotic expansion.
	www.absoluteastronomy.com /encyclopedia/e/ed/edgeworth_series.htm (554 words)

	Maybe this Explains the Economic Cycle... best Edgeworth Series (Site not responding. Last check: 2007-10-08)
		We are sure, that spectacular discovery on analytic methods will follow in the end of the 21st century and will be comparable with achievements of Einstein and his "Relative theory" but in descreet mathematics, theory of games and catastrophes.
		Use of the Edgeworth series to predict energy loss and scattering angle in...
		Edgeworth Series -- from MathWorld Edgeworth Series -- from MathWorld Let a distribution to be approximated be the distribution F_n of standardized sums Y_n={\sum_{i=1}^n (X_i-\bar X)\over\sqrt{\sum_{i=1}^n \sigma^2_X}}.
	ascot.pl /th/Fourier3/Edgeworth-Series.htm (336 words)

	Inventory to the Elliott and Gonzales Family Papers,Mss. Dept., UNC-Chapel Hill. (Site not responding. Last check: 2007-10-08)
		Using the pen name Agricola, he expressed his ideas on slavery in a series of letters which were later collected and published as The Letters of Agricola (1852).
		The collection is arranged in series and subseries as follows: Series 1.
		Harriett Rutledge Gonzales entered Edgeworth School in Baltimore in 1883 and wrote several letters (1883-1886) to her South Carolina family about her educational progress.
	www.lib.unc.edu /mss/inv/e/Elliott_and_Gonzales_Family.html (10265 words)

	Edgeworth Laboratory
		The idea for the Edgeworth Laboratory came to me in 1989 while I was a professor in the Measurement and Evaluation Program at the University of Ottawa.
		The laboratory is named in honor of Professor F. Edgeworth for his foundational work and scholarship in the application of mathematics and mathematical principles to the behavioural sciences.
		Educational and behavioral statistics are very much aligned and many of us work in both fields -- in fact, one of the leading journals is entitled the Journal of Educational and Behavioral Statistics which is jointly published by the American Statistical Association and the American Educational Research Association.
	www.educ.ubc.ca /faculty/zumbo (779 words)

	Francis Edgeworth
		Francis Edgeworth came to study statistics after an education in ancient and modern languages.
		Exactly what Edgeworth did in the years after leaving Oxford is unclear.
		M G Kendall, Francis Ysidro Edgeworth, 1845-1926, in E S Pearson and M G Kendall, Studies in the History of Statistics and Probability (London, 1970), 257-263.
	www.shsu.edu /~icc_cmf/bio/edgeworth.html (660 words)

	Ashok Kumar Bansal - Research Students (Site not responding. Last check: 2007-10-08)
		Abstract: The class of Edgeworth series distributions is used to study the robustness of Bayes estimate and test of significance for the unknown slope parameter of the simple normal linear regression model.
		Abstract: Edgeworth series distributions are used to examine the effects of moderate amount of non-normality in the prior distribution of normal mean on predictive density function, optimum allocation of treatments, sampling inspection plans, Bayes estimates of reliability and reliable life, and hierarchical Bayes predictions.
		Abstract: The dissertation deals with the problem of Bayes estimation and prediction for the distributions belonging to the exponential family, the modified power series distributions and the decapitated generalised negative binomial distributions.
	www.geocities.com /bayesianstats/students.html (357 words)

	Educational and Counselling Psychology, and Special Education - Faculty of Education - UBC
		This laboratory is directed to the use of action theory as a conceptual framework and research method to investigate issues in career development, parent-adolescent communication, family transitions, health, counselling, education, addiction, suicide and other joint human actions and projects.
		Edgeworth Laboratory for Quantitative Educational and Behavioural Science.
		The primary focus of the laboratory is statistical science, measurement theory and practice, and methodology for research and program evaluation.
	www.ecps.educ.ubc.ca /research/labs.html (339 words)

	Financial Markets Group
		After the seminal paper of Jarrow and Rudd (1982), several authors have proposed to use different statistical series expansion to price options when the risk-neutral density is asymmetric and leptokurtic.
		Amongst them, one can distinguish the Gram-Charlier Type A series expansion (Corrado and Su, 1996-b and 1997-b), the log-normal Gram-Charlier series expansion (Jarrow and Rudd, 1982) and the Edgeworth series expansion (Rubinstein, 1998).
		We first re-call the link between the risk-neutral density and moments in a general statistical series expansion framework under the martingale hypothesis.
	fmg.lse.ac.uk /publications/searchdetail.php?wpdid=631 (223 words)

	Serie de Edgeworth (Site not responding. Last check: 2007-10-08)
		La serie del Gramo-Charlier A tiene las características de una extensión asintótica, es decir, los mejores resultados se logran generalmente cuando solamente los primeros pares de términos se utilizan.
		Edgeworth desarrolló una extensión similar como mejoría al teorema de límite central.
		La serie de Edgeworth se desarrolla semejantemente a la serie del Gramo-Charlier A, sólo ésa ahora llama se recoge según energías de n.
	www.yotor.net /wiki/es/se/Serie%20de%20Edgeworth.htm (513 words)

	Ashok Kumar Bansal - Publications (Site not responding. Last check: 2007-10-08)
		In this paper, we study the Bayes forecast for demand and the risk when (a) 'noise' and (b) mean demand rate in a constant process model have moderately non-normal probability distributions.
		Some interesting cases and numerical illustrations are also discussed to bring out their behaviour when the 'true' prior of the unknown parameters is not the conventional normal-gamma distribution.
		The derived expressions are directly applicable to an investigation of the robustness of the Bayes forecast to non-normality in the assumed prior of the unknown mean when the time series is adequately described by a constant process model in which 'noise' is normal with mean zero but variance unknown.
	www.geocities.com /bayesianstats/publications.html (1890 words)

	Footnotes, Books I-III; Bastable: Public Finance: Library of Economics and Liberty
		The belief that the State should be a model employer is rapidly gaining ground, as the partial adoption of the eight-hour day and the acceptance of the Trade Union rate of wages show.
		Edgeworth ingeniously points out that under indirect taxation there will be 'a loss of consumers' rent, which does not occur when the amount is directly subtracted from income,' and therefore regards taxes on commodities as 'more burdensome than direct taxation,' Economic Journal, vii.
		Professor Edgeworth's series of articles on various aspects of incidence are highly important.
	www.econlib.org /library/Bastable/bastbPFNotes.html (13679 words)

	SSRN-Edgeworth on the Foundation of Ethics and Probability by Alberto Baccini
		This paper analyses the foundation of utilitarian ethics and theory of probability in the works of Francis Y. Edgeworth.
		The common root of the disciplines is the notion of "hereditary experience" derived from Herbert Spencer's work.
		Baccini, Alberto, "Edgeworth on the Foundation of Ethics and Probability".
	papers.ssrn.com /sol3/papers.cfm?abstract_id=548602 (200 words)

	ttgapers.com store - The Bootstrap and Edgeworth Expansion (Springer Series in Statistics) - Peter Hall - Product ... (Site not responding. Last check: 2007-10-08)
		Chapter 1 is about the bootstrap, witih almost no mention of Edgeworth expansion; Chapter 2 is about Edgeworth expansion, with scarcely a word about the bootstrap; and Chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properites of the bootstrap.
		The book simultaneously fills two gaps in the literature; it provides a very readable graduate level account of the theory of Edgeworth expansion, and it gives a detailed introduction to the theory of bootstrap methods.
		However the asymptotic results for Edgeworth and Cornish-Fisher expansions provide important insight into the advantages of bootstrap and the special modifications such as bootstrap iteration and various other bootstrap variants for confidence intervals including Efron's BCa method.
	www.ttgapers.com /ttStore-index2-asin-0387945083.html (494 words)

	SSRN-Valid Edgeworth Expansions for the Whittle Maximum Likelihood Estimator for Stationary Long-memory Gaussian Time ...
		In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter theta in Theta subset R^{d_theta).
		Lieberman, Rousseau, and Zucker (2002) (LRZ) establish a valid Edgeworth expansion for the maximum likelihood estimator for stationary long-memory Gaussian models.
		The results given here improve upon those of LRZ in that the results provide an Edgeworth expansion for an asymptotically efficient estimator, as LRZ do, but the error of the expansion is shown to be o(n^{-(s-2)/2}), not o(n^{-1}), for a broad range of models.
	papers.ssrn.com /sol3/papers.cfm?abstract_id=311499 (406 words)

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		The Bayesian approach, on the other hand, is free from such problems and therefore, provides a more convenient and formal framework not only in case of normally distributed disturbances but also in case of non-normal disturbances, which are common for economic and financial data.
		We consider an autoregressive model with distribution of disturbances approximated by an Edgeworth series distribution.
		The posterior odds ratio has been derived for the unit root hypothesis under appropriate prior assumptions for the parameters of the model and the results have been applied to eight real exchange rates.
	www.it.bond.edu.au /seminars/Abstracts/032/Chaturvedi%20-%209%20July%2003.htm (183 words)

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