NIGERIAN JOURNAL OF SCIENCE AND ENVIRONMENT
Journal of the Faculties of Science and Agriculture, Delta State University, Abraka, Nigeria

ISSN: 1119-9008
DOI: 10.5987/UJ-NJSE
Email: njse@universityjournals.org


ON THE GENERALIZED CHARACTERIZATION OF THE BETA DISTRIBUTION OF THE FIRST KIND

DOI: 10.5987/UJ-NJSE.17.105.3   |   Article Number: 71E2AC22   |   Vol.10 (3) - December 2011

Author:  Igabari J. N.

Keywords: Beta function, Beta distribution, limiting form, quantiles, points of inflexion

In this work, we demonstrate that momental measures could be used to characterize the Beta distribution of the first kind. Furthermore, we show that the characterization is unique, and this distribution degenerates into Uniform distribution or the Gama distribution, depending on the choice of its parameters.

Athreya, K. B and Lahiri, S. N. (2006) Texts and Readings in Mathematics. Vol. 41:

Probability Theory, Hindustan Book Agency, New Delhi. Chung, K. L (1977) Elementary Probability Theory with Stochastic Process. Springer- Verlag, New York.

Durrett, R (2004) Probability: Theory and Examples, 3rd Edition, Duxbury Press, Califonia.

Rahman, N. A (1978) A Course in Theoretical Statistics, Charles Griffin and Co Ltd., London.

Stuart, A and Ord, J. K. (1998) Kendall’s Advanced Theory of Statistics, Vol. 1 (Distribution Theory) 6th Edition, Oxford University Press, New York.