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Journal of Applied Sciences

Year: 2004 | Volume: 4 | Issue: 4 | Page No.: 554-560
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Research Article

A Note on Mixed Distributions Involving Two Related Negative Hypergeometric Distributions

Titi Obilade

ABSTRACT

The study considered the mixed version of distributions of likelihood functions of two related hypergeometric distributions. This arises from a consideration of sampling without replacement from a finite population with balls of different colours and in different proportions but stopping only after some sufficient specific (possibly equal) number of balls of different colours might have been obtained. The resulting sample may be large or small relative to the specific stopping value depending mainly on the actual proportions of the different balls. Our interest is in the distribution of two likelihood functions, being normalised quotients of maximal or the minimal distribution with the distribution for draws for the rarest of the colours. With the aid of some simple recurrence relations and identities we obtain, in the case of two colours with the possibility of some inflation by some non-specific extraneous factors, the moments of the resulting distributions for the necessary number of draws. We also drive necessary equations for the estimation of the relevant parameters.
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REFERENCES

  1. Cohen, A.C., 1996. A note on certain discrete mixed distributions. Biometrics, 22: 566-572.
  2. Zhang, Z., B.A. Burtness and D. Zelterman, 2000. The maximum negative binomial distribution. J. Statistics Plann. Inference, 87: 1-19.
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  4. Gradshteyn, I.S. and I.M. Ryzhik, 1980. Table of Integrals Series and Products. Academy Press, New York, USA.

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