Authors

  • Yusupova A.K.
    Candidate Of Physical And Mathematical Sciences, Associate Professor, Fergana State University, Uzbekistan
  • Gafforov R.A.
    Teacher, Fergana State University, Uzbekistan

DOI:

https://doi.org/10.37547/tajiir/Volume03Issue06-15

Keywords:

Negative hypergeometric distribution (the Romanovsky distribution) Erlang distribution minimax problem.

Abstract

The paper considered a refinement of the theorem for a negative-hypergeometric distribution( the Romanovsky distribution), i.e., convergence over variation of the Romanovsky distribution by Erlang distributions. The theorem is proved by the direct asymptotic method.

References

Prokhorov Yu.V. Asymptotic behavior of the binomial distribution. Successes of mathematical sciences, vol. VIII, no. 3 (1953), pp. 135-142.

Romanovsky V.I. Ordered samples from the same continuous population. Proceedings of the Institute of Mathematics and Mechanics. Tashkent, 1949, pp. 5-19.

Loev M. Probability theory. Moscow: Foreign Literature Publishing House. 1962. from. 268.

Hasting N., Peacock J. Handbook of statistical distributions. Moscow: Statistics, 1980.

Azlarov T.A., Yusupova A.K. The minimax problem of the limiting behavior of the V.I.Romanovskii distribution. Reports of the Academy of Sciences of the UzSSR, No. 8 (1990), pp. 4-5.

Yusupova A.K. Asymptotic study of the behavior of the Romanovsky distribution. Dep. at VINITI. B-No. 7547.

Yusupova A.K. Limit theorems for one Romanovskii distribution and their refinement. Collection of articles: Asymptotic problems of probability theory and mathematical statistics, Tashkent: Fan. 1990, S. 157-162.