Non-Normal Bivariate Distributions with Normal Marginals

Kowalski, Charles J.

doi:10.2307/2683630

Cited by 20 publications

(11 citation statements)

References 19 publications

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“…18 18 The normality of each univariate random variable is a necessary but not sufficient condition. In fact, Kowalski (1973) has provided several examples of nonnormal bivariate distributions for which the marginal distributions are both normal. …”

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confidence: 99%

MultiFactor Valuation of Floating Range Notes

Nunes¹

2003

Mathematical Finance

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Under a one-factor Gaussian Heath-Jarrow-Morton model, Turnbull (1995) as well as Navatte and Quittard-Pinon (1999) have provided explicit pricing solutions for range notes contracts. The present paper generalizes such closed-form solutions for the context of a multifactor Gaussian HJM framework.KEY WORDS: Gaussian HJM multifactor models, change of probability measure, bivariate normal distribution, interest rate digital options, range notes Manuscript

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confidence: 99%

MultiFactor Valuation of Floating Range Notes

Nunes¹

2003

Mathematical Finance

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“…Explicit constructions using the copulas in Exercises 2.4, 2.12, and 3.11, Example 3.12, and Sect. 3.3.1 can be found in (Kowalski 1973), and one using the copula C 1 2 from Exercise 2.10 in (Vitale 1978).…”

Section: Theorem 233 Sklar's Theorem Let H Be a Joint Distributiomentioning

confidence: 99%

An Introduction to Copulas

2006

Springer Series in Statistics

350

145

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“…However, under certain conditions multivariate joint distributions are not normal even when their univariate marginal distributions are (Kowalski 1973). Still, my bias arising from basing Hotelling's T2 statistic on a non-normal, multivariate, joint distribution can be lessened by using large numbers in the analysis.…”

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confidence: 99%

Multivariate Analysis as a Means of Comparing Growth in Fish

Bernard¹

1981

Can. J. Fish. Aquat. Sci.

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e~p o r t , OR 97365, &rYA BERNARD, D. R. 1981. Multivariate analysis as a means of comparing growth in fish. Can. J. Fish. Aquat. Sci. 38: 233-236.The Hotelling's T~ is described as a test for differences between like von Bertalanffy growth parameters estimated from two fish groups when these parameters are correlated.Equations to calculate 7 " ' are presented as are equations to modify T2 to an F statistic for use in testing. Simultaneous confidence intervals and critical F values are described to separate effects of parameters on observed differences in growth. Assumptions made by the T2 technique are discussed, as are ways in which any bias caused by violating these assumptions is lessened. Two numerical examples concerning growth differences among groups of Pacific ocean perch (Sehastes alutus) are provided. Growth of male and of female perch captured off the Columbia River is different with L, being the most statistically significant parameter and P, the Beast. Growth of male perch captured off Vancouver Island and off the Columbia River is also different with only L, statistically significant. , 1981. Multivariate analysis as a means of comparing growth in fish, Can. J. Fish. Aquat. Sci. 38: 233-236. Le prksent article contient une description du T2 de Hotelling comme test des diffbrences entre paramGtres de croissance de von Bertalanffy semblables estimts chez deux groupes de poissons et quand ces parametres sont reliCs. On y resente les Cquations servant B calculer P T' ainsi que les Cquations pernettant de modifier T en une statistique F pour usage dans le test. On dCcHit les intervalles de confiance simultanks et les valeurs critiques de I: afin de siparer les effets des paramktres sur Ies differences de croissance observkes. Les hypothises sous-tendant la technique du T2, ainsi que les moyens d'attknuer tout biais pouvant risulter de la violation de ces hypothkses sont examinbs. Deux exemples numkriques de differences de croissance p a m i des groupes de sChastes B longue michoire (Sebastes ctfutu.~) sont prQentCs. Les &bastes miles et femelles capturis au large dm fleuve Columbia diffkrent dans leur croissance, H , , Ctant le parametre le plus significatif i l'analyse statistique et to, le parametre le moins significatif. La croissance des sCbastes m3es capturbs au large de I'ile Vancouver et au Iarge du Weuve Columbia differe Cgalement, L, seul Ctmt statistiquement significatif.

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Non-Normal Bivariate Distributions with Normal Marginals

Cited by 20 publications

References 19 publications

MultiFactor Valuation of Floating Range Notes

MultiFactor Valuation of Floating Range Notes

An Introduction to Copulas

Multivariate Analysis as a Means of Comparing Growth in Fish

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