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On Asymptotic Testing of Equality of Parameters of K Exponential Family of Distributions
Patel S. R.1
Section:Research Paper, Product Type: Isroset-Journal
Vol.5 ,
Issue.6 , pp.177-182, Dec-2018
CrossRef-DOI: https://doi.org/10.26438/ijsrmss/v5i6.177182
Online published on Dec 31, 2018
Copyright © Patel S. R. . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: Patel S. R., “On Asymptotic Testing of Equality of Parameters of K Exponential Family of Distributions,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.177-182, 2018.
MLA Style Citation: Patel S. R. "On Asymptotic Testing of Equality of Parameters of K Exponential Family of Distributions." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.6 (2018): 177-182.
APA Style Citation: Patel S. R., (2018). On Asymptotic Testing of Equality of Parameters of K Exponential Family of Distributions. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(6), 177-182.
BibTex Style Citation:
@article{R._2018,
author = {Patel S. R.},
title = {On Asymptotic Testing of Equality of Parameters of K Exponential Family of Distributions},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {12 2018},
volume = {5},
Issue = {6},
month = {12},
year = {2018},
issn = {2347-2693},
pages = {177-182},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=991},
doi = {https://doi.org/10.26438/ijcse/v5i6.177182}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i6.177182}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=991
TI - On Asymptotic Testing of Equality of Parameters of K Exponential Family of Distributions
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Patel S. R.
PY - 2018
DA - 2018/12/31
PB - IJCSE, Indore, INDIA
SP - 177-182
IS - 6
VL - 5
SN - 2347-2693
ER -
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Abstract :
In this paper attempt has been made to obtain the asymptotic tests for testing the equality of parameters involved in several exponential family of distributions. Any exponential family has been reduced to naturalized form if it is not so. The naturalized exponential family is asymptotically reduced to multivariate normal distribution with the use of well-known multivariate central limit theorem and the test for equality of components of multivariate normal gives equivalently the test for equality of parameters of the family, which turns out as Uniformly Most Powerful (UMP) Invariant (UMPI) test. This general result has been applied to some specific distributions such as Binomial, Poisson, Exponential, Gamma distributions as particular cases of exponential family.
Key-Words / Index Term :
Exponential family of distributions, asymptotic distribution, Asymptotic UMPI test
References :
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[3] Kambo NS, Awad AM, “Testing equality of location parameters of K exponential distributions”, Comm Statist Theory Methods Vol. 14, pp.567–85, 1985
[4] Keating JP, Glaser,RE, Ketchum NS, “Testing hypotheses about the shape parameter of a gamma distribution”, Technometrics. Vol.32, pp.67–82, 1990
[5] Lehmann EL,” Testing Statistical Hypotheses”, Springer, New York, 2005
[6] Muirhead RJ, “On the Distribution of the Likelihood Ratio Test of Equality of Normal Populations”, The Canadian Journal of Statistics, Vol.10, pp.59–62, 1982
[7] Patel, S.R., “Asymptotic tests for truncated parameters of several one-parameter truncation family of distributions”, Research and Reviews: Journal of Statistics, Vol. 7, issue.2, pp.35-41, 2018
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