2000
DOI: 10.1524/zkri.2000.215.12.718
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Edgeworth series expansion of the truncated Cauchy function and its effectiveness in the study of atomic heterogeneity

Abstract: The effectiveness of a near Gaussian distribution, namely the Edgeworth Series representation of a truncated Cauchy distribution in studying heterogeneous cases has been studied for space group P¯1. Though moments do not exist for a Chauchy distribution a truncated Cauchy distribution has finite moments whose value depends on the truncation limit. A number of real examples with varying degrees of heterogeneity have been considered and the effect of truncation at various cut-off values has been studied. This ap… Show more

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“…1, eqn (1)) and probability density function (PDF; eqn (2)) are modified by the location parameter, x 0 , and the scale parameter, γ . 29 As a stable distribution, the Cauchy distribution has applications in chemistry and physics, 30–32 geology, 33 engineering, 34 and economics. 35 …”
Section: Introductionmentioning
confidence: 99%
“…1, eqn (1)) and probability density function (PDF; eqn (2)) are modified by the location parameter, x 0 , and the scale parameter, γ . 29 As a stable distribution, the Cauchy distribution has applications in chemistry and physics, 30–32 geology, 33 engineering, 34 and economics. 35 …”
Section: Introductionmentioning
confidence: 99%