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Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function

A. Loganathan1 , S. Mari Chelvi2 , M. Uma3

  1. Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, India.
  2. Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, India.
  3. Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, India.

Correspondence should be addressed to: aln_24@rediffmail.com.


Section:Research Paper, Product Type: Isroset-Journal
Vol.4 , Issue.5 , pp.13-16, Oct-2017


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.1316


Online published on Oct 30, 2017


Copyright © A. Loganathan, S. Mari Chelvi, M. Uma . 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: A. Loganathan, S. Mari Chelvi, M. Uma, “Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.13-16, 2017.

MLA Style Citation: A. Loganathan, S. Mari Chelvi, M. Uma "Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function." International Journal of Scientific Research in Mathematical and Statistical Sciences 4.5 (2017): 13-16.

APA Style Citation: A. Loganathan, S. Mari Chelvi, M. Uma, (2017). Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function. International Journal of Scientific Research in Mathematical and Statistical Sciences, 4(5), 13-16.

BibTex Style Citation:
@article{Loganathan_2017,
author = {A. Loganathan, S. Mari Chelvi, M. Uma},
title = {Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {10 2017},
volume = {4},
Issue = {5},
month = {10},
year = {2017},
issn = {2347-2693},
pages = {13-16},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=479},
doi = {https://doi.org/10.26438/ijcse/v4i5.1316}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v4i5.1316}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=479
TI - Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - A. Loganathan, S. Mari Chelvi, M. Uma
PY - 2017
DA - 2017/10/30
PB - IJCSE, Indore, INDIA
SP - 13-16
IS - 5
VL - 4
SN - 2347-2693
ER -

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Abstract :
The inverse Maxwell distribution is the probability distribution of the reciprocal of the Maxwell random variable. This distribution has applications in reliability and life testing. In this paper, Bayes estimator of the parameter in the inverse Maxwell distribution is derived employing Jeffreys non-informative prior under weighted quadratic loss function. The Bayes estimator in this case is the minimax estimator. Efficiency of the Bayes estimator is compared with the maximum likelihood estimator. Application of the inverse Maxwell distribution to a real life situation is also studied.

Key-Words / Index Term :
Bayes estimator, Inverse Maxwell distribution, Jeffreys prior, Maximum likelihood estimator

References :
[1] L. Boltzmann, “Further Studies on Thermal Equilibrium among Gas Molecule” Conference Reports of the Imperial Academy of Sciences, Vienna, Mathematical and Natural Sciences class, 66, pp. 275-370, 1872.
[2] I.J. Good., R.A. Gaskins., “Density Estimation and Bump-hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data”, Journal of the American Statistical Association, 75, pp.42-56, 1980.
[3] P.M. Lee, “ Bayesian Statistics: An Introduction”, Second Edition, Arnold Publication, 1997.
[4] E.L. Lehmann, “Theory of Point Estimation”, John Wiley, New York, 1983.
[5] A. Loganathan., S. Mari Chelvi., “Estimation of Parameter in Inverse Maxwell Distribution”, Communications in Statistics - Simulation and Computation (communicated), 2017a.
[6] J.C. Maxwell, “Illustrations of the Dynamical Theory of Gases. Part I. On the Motions and Collisions of Perfectly Elastic Spheres”, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 4th Series, Vol.19, pp.19-32, 1860a.
[7] M. Rajagopalan., P. Dhanavanthan., “Statistical Inference”, PHI Learning Private Limited, India, 2012.
[8] K.L. Singh., R.S. Srivastava., “Inverse Maxwell Distribution as a Survival Model, Genesis and Parameter Estimation”, Research Journal of Mathematical and Statistical Sciences, Vol.2 (7), pp.23-28, 2014.

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