On Testing of Multiple Hypotheses of Continuous Probability Distributions Arranged into Two Groups
DOI:
https://doi.org/10.51408/1963-0107Keywords:
Neyman-Pearson procedure, Continuous probability distribution, Probability density function, Hypothesis testing, Error probabilities, ReliabilitiesAbstract
The optimal Neyman-Pearson procedure of detection is investigated for models characterized by four continuous probability distributions arranged into two groups considered as hypotheses. It is worthy to note that the case of three discrete probability distributions arranged in two groups was studied by Haroutunian and Yesayan in [1]. The Neyman-Pearson theorem holds immense importance when it comes to solving problems that demand decision making or conclusions to a higher accuracy.
References
E. A. Haroutunian and A. O. Yesayan, “A Neyman-Pearson proper way to universal testing of multiple hypotheses formed by groups of distributions”, Mathematical Problems of Computer Sciences, vol. 54, pp. 18-33, 2020.
D. R. Cox, “Tests of separate families of hypotheses” In Proceeding 4th Berkley Simp. Math. Statist. Prob., University of Callifornia Press, Berkelly, pp. 105-123, 1961.
D. R. Cox, “Further results on tests of separate families of hypotheses”, Journal of the Royal Statist. Society: Serie B, vol. 24, issue 2, pp. 406-424, 1962.
D. R. Cox, “A return to an old paper: Tests of separate families of hypotheses”, Journal of the Royal Statist. Society: Serie B, vol. 75, issue 2, pp. 207-2015, 2013.
G. Tusn´ady, “On asymptotically optimal tests”, Annals of Statatistics, vol. 5, no. 2, pp. 385-393, 1977.
W. Hoeffding, “Asymptotically optimal tests for multinomial distributions,” The Annals of Mathematical Statistics, vol. 36, pp. 369–401, 1965.
E. A. Haroutunian, “Reliability in multiple hypotheses testing and identification problems” Nato Science Series III, Computer and System Sciences, vol.198, IOS Press, pp. 189-201, 2003.
E. A. Haroutunian, P. M. Hakobyan and F. Hormosi-nejad, “On two-stage LAO testing of multiple hypotheses for the pair of families of distributions”, Journal of Statistics and Econometrics Methods , vol. 2, no. 2, pp. 127-156, 2013.
A. O. Yesayan and H. Z. Gevorgyan,On two-stage testing of multiple hypotheses testing concerning continuous random variable , Europian academia: Collection of scientific articles, vol. 7, pp. 294-299, 2016.
A. A. Borovkov, Mathematical Statistics (in Russian). Nauka, Novosibirsk, 1997.
B. C. Levy, Principles of Signal Detection and Parameter Estimation, Springer, 2008.
H. van Trees, Detection, Estimation and Modulation Theory, pt.1 New York, Wiley, 1968.
I. Csiszár and G. Longo, “On the error exponent for source coding and for testing simple statistical hypotheses”, Studia Sc. Math. Hungarica, vol. 6, pp. 181–191, 1971.
I. Csiszár and P. Shields, “ Information theory and statistics: A tutorial”, Foundations and Trends in Communications and Information Theory, vol. 1, no. 4, 2004.
G. Longo and A. Sgarro, “ The error exponent for the testing of simple statistical hypotheses: A combinatorial approach”, Journal of Combinatorics and Informational System Science, vol. 5, no. 1, pp. 58-67, 1980.
E. A. Haroutunian and P. M. Hakobyan, “On Neyman-Pearson principle in multiple hypotheses testing”, Mathematical Problems of Computer Sciences, vol. XL, pp. 34-37, 2013.
T. M. Cover and J. A. Thomas, Elements of Information Theory, Second Edition, New York, Wiley, 2006.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Aram O. Yesayan
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
