Minimax Estimator on Binomial Distribution

Volume 7, Issue 4, August 2022     |     PP. 60-66      |     PDF (1188 K)    |     Pub. Date: July 31, 2022
DOI: 10.54647/mathematics11340    106 Downloads     4968 Views  

Author(s)

Zul Amry, Department of Mathematics, State University of Medan, Indonesia
Sisti Nadia Amalia, Department of Mathematics, State University of Medan, Indonesia

Abstract
This paper discusses the minimax estimator of parameter for binomial distribution. The likelihood function is constructed based on the probability function of the Binomial distribution. The posterior distribution is obtained from the joint of the likelihood function and prior distribution. Furthermore, the Bayes estimator is obtained based on the posterior mean and provide the constancy of the risk of Bayes the minimax estimator can be concluded.

Keywords
Bayes theorem, binomial distribution, minimax estimator

Cite this paper
Zul Amry, Sisti Nadia Amalia, Minimax Estimator on Binomial Distribution , SCIREA Journal of Mathematics. Volume 7, Issue 4, August 2022 | PP. 60-66. 10.54647/mathematics11340

References

[ 1 ] Abushal, T. A. (2019). Bayesian Estimation of the Reliabelity Characteristic of Shanker Distribution. Journal of the Egyptian Mathematical Society, 1–15.
[ 2 ] Ayed, F. et al, (2021). Consistent Estimation of Small Masses in Feature Sampling. Journal of Machine Learning Research, 22, 1–28.
[ 3 ] Bain, L. J. and Engelhardt, M., (2006). Introduction to Probability and Mathematical Statistics, 2nd, Belmont, California: Duxbury Press.
[ 4 ] Borisov, A., (2021). Minimax Estimation in Regression under Sample Conformity Constraints. Mathematics MDPI, 1–21.
[ 5 ] Debnath, M. R. et al, (2021). Minimax Estimation of the Scale Parameters of the Laplace Double Exponential Distribution. International Journal of Statistical Sciences, 21(1), 105–116.
[ 6 ] Fatima, K., Ahmad, S.P., (2018). Bayesian Approach in Estimation of Shape Parameter of the Exponentiated Moment Exponential Distribution. Journal of Statistical Theory and Applications, 17(2), 359–374.
[ 7 ] Hasan, M. R., (2019). Minimax Estimation of the Scale Parameter of Laplace Distribution under Modified Linear Exponential (MLINEX) Loss Function. J. Sci. Res., 11 (3), 273–284.
[ 8 ] Jeon, Y.E., Kang, S. B., (2020). Bayesian Estimation for the Exponential Distribution Based on Generalized Multiply Type-II Hybrid Cencoring. Communications for Statistical Applications and Methods, 27(4), 413–430.
[ 9 ] Li, L., (2016). Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions. American Journal of Theoretical and Applied Statistics, 5(4), 202–207.
[ 10 ] Okasha, H. M., (2019). E-Bayesian Estimation for the Exponential Model Based on Record Statistics. Journal of Statistical Theory and Applications, 18(3), 236–243.
[ 11 ] Osu, B. O, Eggege, S. O, Ekpeyong, E. J., (2017). Application of Generalizad Binomial Distribution Model for Option pricing. American Journal of Applied Mathematics and Statistics, 5(2), 62–71.
[ 12 ] Podder, C. K., (2020). Minimax Estimation of Scale Parameter in a CLass of Life Time Distributions for Different Loss Functions. International Journal of Statistical Sciences, 20(2), 85–98.
[ 13 ] Rasheed, H. A., Khalifa, Z. N., (2016). Semi-Minimax Estimators of Maxwell Distribution under New Loss Function. Mathematics and Statistics Journal, 2(3), 16–22.
[ 14 ] Zul Amry, (2020). Bayesian Estimate of Parameters for ARMA Model Forecasting. Tatra Mountains Mathematical Publication, Vol.75, 23-32.
[ 15 ] Zul Amry, (2021). Bayes Estimator for inverse Gaussian Distribution with Jeffrey’s Prior. SCIREA Journal of Mathematics, Vol. 6, Issue 4, 44-50.