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Lookup NU author(s): Dr Jordan Stoyanov
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Let F be a probability distribution function with density f. We assume that (a) F has finite moments of any integer positive order and (b) the classical problem of moments for F has a nonunique solution (F is M-indeterminate). Our goal is to describe a Stieltjes class S = {f(epsilon) = f [1 + epsilonh], epsilon is an element of [-1, 1]}, where h is a 'small' perturbation function. Such,) all sharing the same a class S consists of different distributions F-epsilon (f(epsilon) is the density of F, moments as those of F, thus illustrating the nonuniqueness of F, and of any F-epsilon in terms of the moments. Power transformations of distributions such as the normal, log-normal and exponential are considered and for them Stieltjes classes written explicitly. We define a characteristic of S called an index of dissimilarity and calculate its value in some cases. A new Stieltjes class involving a power of the normal distribution is presented. An open question about the inverse Gaussian distribution is formulated. Related topics are briefly discussed.
Author(s): Stoyanov J
Publication type: Article
Publication status: Published
Journal: Journal of Applied Probability
Year: 2004
Volume: 41A
Pages: 281-294
Print publication date: 01/01/2004
ISSN (print): 0021-9002
ISSN (electronic): 1475-6072
Publisher: Applied Probability Trust
URL: http://dx.doi.org/10.1239/jap/1082552205
DOI: 10.1239/jap/1082552205
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