Isaac Scientific Publishing

Journal of Advanced Statistics

On Minimum Variance Unbiased Estimator of the Parameter in S(d) Distribution

Download PDF (550 KB) PP. 71 - 75 Pub. Date: June 13, 2016

DOI: 10.22606/jas.2016.12003

Author(s)

  • Nanjundan G*
    Department of Statistics, Bangalore University, Bangalore 560 056, India
  • Suresh R
    Department of Statistics, Karnatak University, Dharwad 580 003, India

Abstract

A new class of discrete distributions analogous to Burr family has been chararacterized by Sreehari (2010)[1]. The d-th member of this class is structurally equivalent to Poisson distribution. Nanjundan and Naika (2012, 2015)[2] [3] have discussed the maximum likelihood and the moment estimators of the parameter in the distribution. In this paper, a minimum variance unbiased estimator of the parameter is obtained and its properties are discussed. Further, an asymptotic comparison of these three estimators is done.

Keywords

Discrete distribution, maximum likelihood estimator, moment estimator, mimimum variance unbiased estimator, CAN, ARE.

References

[1] M. Sreehari, “On a class of discrete distributions analogous to burr family,” Journal of Indian Statistical Association, 2010.

[2] G. Nanjundan and T. R. Naika, “Estimation of parameter in a new discrete distribution analogous to burr family,” in Proceedings of the International Conference on Information Technology and Computer Application Engineering. Lin, Sung, and Yao (Eds.), Taylor and Francis, London, 2014, pp. 399–402.

[3] G. Nanjundan and T. R. Naika, “An asymptotic comparison of maximum likelihood and moment estimators of parameter in a new discrete distribution analogous to a burr distribution,” ProbStat Forum, vol. 8, October, 2015.

[4] S. Chakraborty, “Generating discrete analogues of continuous probability distributions: A survey of methods and constructions,” Journal of Statistical Distributions and Applications, vol. 2, no. 6, 2015.

[5] P. J. Bickel and K. A. Doksum, Mathematical Statistics. Prentice Hall, 2001.