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Two characterisations of a gamma mixture distribution

  • M. Gharib (a1)
Abstract

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.

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[1]Aczel, J., Lectures on functional equations and their applications (Academic Press, New York, 1966).
[2]Ashton, W.D., ‘Distribution for gaps in road traffic’, Inst. Maths. and Applics. 7 (1971), 3746.
[3]Durling, F.C., Bivariate Probit, Logit and Burnt Analysis, THEMIS, Report No. 41 (Stat. Dept., Southern Methodist Univ., Dallas, Texas, 1969).
[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.
[5]Johnson, N.L. and Kotz, S., Distributions in statistics 4 (Wiley, New York, 1972).
[6]Marshall, A.W. and Olkin, I., ‘A generalized bivariate exponential distribution’, J. Appl. Probab. 4 (1967), 291302.
[7]O'Neill, T.J. and O'Neill, H.C., ‘A gamma model for extra-binomial variation in dilution assays’, Biometrics 49 (1993), 237242.
[8]Prentice, R.L., ‘Correlated binary regression with covariates specific to each binary observation’, Biometrics 44 (1988), 10331048.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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