Mixtures, myths and kurtosis

MacGillivray H.L. and Balanda K.P. (1988) Mixtures, myths and kurtosis. Communications in Statistics - Simulation and Computation, 17 3: 789-802. doi:10.1080/03610918808812695

Author MacGillivray H.L.
Balanda K.P.
Title Mixtures, myths and kurtosis
Journal name Communications in Statistics - Simulation and Computation   Check publisher's open access policy
ISSN 1532-4141
Publication date 1988-01-01
Sub-type Article (original research)
DOI 10.1080/03610918808812695
Open Access Status Not yet assessed
Volume 17
Issue 3
Start page 789
End page 802
Total pages 14
Language eng
Subject 2611 Modelling and Simulation
2613 Statistics and Probability
Abstract Kurtosis, usually as measured by the standardised fourth central moment, has been examined on a number of occasions by observing the effect of contaminating the distribution, that is, mixing in another distribution. However, superficial treatment can lead, and indeed has led, to misunderstandings. This paper considers, firstly for a symmetric distribution contaminated at two points symmetrically placed around its centre and then for a mixture of two continuous symmetric distributions, the behaviour of three measures of kurtosis. This is done in general and not just as the mixing proportion tends to zero as in the influence function approach. It is seen that when both scale and kurtosis change, the latter is not necessarily intuitive. It is also illustrated that parameter interpretation in terms of distributional properties such as shape can be misleading without the use of the appropriate distributional partial ordering.
Keyword centre
influence function
partial orderings
symmetric distributions
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
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Citation counts: Scopus Citation Count Cited 2 times in Scopus Article | Citations
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