Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T02:40:56.339Z Has data issue: false hasContentIssue false

Two characterisations of a gamma mixture distribution

Published online by Cambridge University Press:  17 April 2009

M. Gharib
Affiliation:
Mathematics DepartmentFaculty of ScienceAin Shams UniversityCairoEgypt
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Two characterisations are obtained for a gamma mixture distribution. The first is a generalisation of a result of Engel, Zijlstra and Philips [4] and the second based on Gumbel's bivariate exponential distribution. The two characterisatio are of direct relevance to some practical problems.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Aczel, J., Lectures on functional equations and their applications (Academic Press, New York, 1966).Google Scholar
[2]Ashton, W.D., ‘Distribution for gaps in road traffic’, Inst. Maths. and Applics. 7 (1971), 3746.CrossRefGoogle Scholar
[3]Durling, F.C., Bivariate Probit, Logit and Burnt Analysis, THEMIS, Report No. 41 (Stat. Dept., Southern Methodist Univ., Dallas, Texas, 1969).CrossRefGoogle Scholar
[4]Engel, J., Zijlstra, M. and Philips, N.V., ‘A characterization of the gamma distribution by the negative binomial distribution’, J. Appl. Probab. 17 (1980), 11381144.CrossRefGoogle Scholar
[5]Johnson, N.L. and Kotz, S., Distributions in statistics 4 (Wiley, New York, 1972).Google Scholar
[6]Marshall, A.W. and Olkin, I., ‘A generalized bivariate exponential distribution’, J. Appl. Probab. 4 (1967), 291302.CrossRefGoogle Scholar
[7]O'Neill, T.J. and O'Neill, H.C., ‘A gamma model for extra-binomial variation in dilution assays’, Biometrics 49 (1993), 237242.CrossRefGoogle ScholarPubMed
[8]Prentice, R.L., ‘Correlated binary regression with covariates specific to each binary observation’, Biometrics 44 (1988), 10331048.CrossRefGoogle ScholarPubMed