Abstract
In this paper, we review the literature on the extensions of the Lukacs’ classical characterization of the gamma distribution and propose several new extensions.
Research partially supported by NSERC of Canada, grant no. A-8792.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bernstein, S., Sur une proprieté charactéristique de la loi de Gauss. Trans. Leningrad Polytechn. Inst. 3 (1941), 21–22.
Findeisen, P., A simple proof of a classical theorem which characterizes the gamma distribution. Ann. Statist. 6 (1978), 1165–1167.
Griffiths, R.C., Infinitely divisible multivariate gamma distributions. Sankyā A, 32 (1970), 393–404.
Kagan, A.M., Linnik, Yu.V. and Rao, C.R., Characterization Problems in Mathematical Statistics. John Wiley and Sons, New York/London/Sydney/Toronto 1973.
Lukacs, E., A characterization of the gamma distribution. Ann. Math. Statist., 26 (1955), 319–324.
Lukacs, E., Characterization of populations by properties of suitable statistics. Proc. Third Berkeley Symposium on Math. Stat. and Prob., Univ. of Calif. Press, Berkeley, (1956), 195–214.
Lukacs, E., Stochastic Convergence, 2nd ed., Academic Press, New York/San Francisco/London 1975.
Lukacs, E., A characterization of a bivariate gamma distribution. Multivariate Analysis-IV, North-Holland Publishing Co., Amsterdam/Oxford/New York 1977.
Lukacs, E. and King, E.P., A property of the normal distribution. Ann. Math. Statist., 25 (1954), 389–394.
Lukacs, E. and Laha, R.G., Applications of Characteristic Functions. Charles Griffin & Co., Ltd., London, 1964.
Marsaglia, G. Extension and applications of Lukacs’ characterization of the gamma distribution. Proc. Symposium Stat. & Related Topics, Carleton University, Ottawa, Oct. 24–26 (1974), 9.01–9.13.
Olkin, I. and Rubin, H., A characterization of the Wishart distribution. Ann. Math. Statist. 33 (1962), 1272–1280.
Pitman, E.J.G., The ‘closest estimates’ of statistical parameters, Proc. Camb. Phil. Soc., 44 (1937), 212–222.
Shanbhag, D.N., An extension of Lukacs’ result. Proc. Camb. Phil. Soc. 69 (1971), 301–303.
Vere-Jones, D., The infinite divisibility of a bivariate gamma distribution. Sankyā A 29 (1967), 421–422.
Wang, Y.H. and Chang, S.A., A new approach to the nonparametric tests of exponential distribution with unknown parameters. The Theory and Applications of Reliability II 235–258, Academic Press, Inc., New York/San Francisco/London 1977.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Wang, Y.H. (1981). Extensions of Lukacs’ characterization of the gamma distribution. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097323
Download citation
DOI: https://doi.org/10.1007/BFb0097323
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10823-8
Online ISBN: 978-3-540-36785-7
eBook Packages: Springer Book Archive