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Shrinkage Estimator of the Parameters of Normal Distribution Based On K- Record Values

Vishal Mehta1

Section:Research Paper, Product Type: Isroset-Journal
Vol.4 , Issue.1 , pp.1-5, Feb-2017


Online published on Feb 06, 2017


Copyright © Vishal Mehta . 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: Vishal Mehta, “Shrinkage Estimator of the Parameters of Normal Distribution Based On K- Record Values,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.1, pp.1-5, 2017.

MLA Style Citation: Vishal Mehta "Shrinkage Estimator of the Parameters of Normal Distribution Based On K- Record Values." International Journal of Scientific Research in Mathematical and Statistical Sciences 4.1 (2017): 1-5.

APA Style Citation: Vishal Mehta, (2017). Shrinkage Estimator of the Parameters of Normal Distribution Based On K- Record Values. International Journal of Scientific Research in Mathematical and Statistical Sciences, 4(1), 1-5.

BibTex Style Citation:
@article{Mehta_2017,
author = {Vishal Mehta},
title = {Shrinkage Estimator of the Parameters of Normal Distribution Based On K- Record Values},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2017},
volume = {4},
Issue = {1},
month = {2},
year = {2017},
issn = {2347-2693},
pages = {1-5},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=316},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=316
TI - Shrinkage Estimator of the Parameters of Normal Distribution Based On K- Record Values
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Vishal Mehta
PY - 2017
DA - 2017/02/06
PB - IJCSE, Indore, INDIA
SP - 1-5
IS - 1
VL - 4
SN - 2347-2693
ER -

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Abstract :
In this paper, we discusses the problem of estimating the parameters of normal distribution based on k- record values in presence of guessed value (or apriori) of the parameters under investigation. We have suggested shrinkage estimators for estimating the parameters and based on best linear unbiased estimator (BLUE). The expressions of biases and mean squared errors (MSEs) of the suggested estimators are obtained. Under some realistic conditions it is shown that the proposed shrinkage estimators are better than [15] estimators.

Key-Words / Index Term :
Best linear unbiased estimation; K- record values; Minimum mean square estimator; Normal distribution; Shrinkage estimator

References :
[1] B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, “Records”, Wiley, New York-1998, ISBN: 978-0-471-08108-1.
[2] B. N. Pandey and B. P. Singh, “On Estimation of Population Variance in Normal Distribution”, Journal of Scientific Research, Volum-27, Page (221-225), 1977.
[3] Housila P. Singh and Vishal Mehta, “An Improved Estimation of Parameters of Morgenstern Type Bivariate Logistic Distribution Using Ranked Set Sampling”, STATISTICA, Volum-73, Issue-4, Page No (437-461), 2013.
[4] Housila P. Singh and Vishal Mehta, “An Alternative Estimation of the Scale Parameter for Morgenstern Type Bivariate Log-Logistic Distribution Using Ranked Set Sampling”, Journal of Reliability and Statistical Studies, Volum-7, Issue-1, Page No (19-29), 2014.
[5] Housila P. Singh and Vishal Mehta, “Linear shrinkage estimator of scale parameter of Morgenstern type bivariate logistic distribution using ranked set sampling”, Model Assisted Statistics and Applications (MASA), Volum-9, Page No (295-307), 2014.
[6] Housila P. Singh and Vishal Mehta, “Estimation of Scale Parameter of a Morgenstern Type Bivariate Uniform Distribution Using Censored Ranked Set Samples”, Model Assisted Statistics and Applications (MASA), Volum-10, Page No (139-153), 2015.
[7] Housula P. Singh and Vishal Mehta, ”Some Classes of Shrinkage Estimators in the Morgenstern Type Bivariate Exponential Distribution Using Ranked Set Sampling”, Hacettepe Journal of Mathematics and Statistics, Volum-45, Issue-2, Page No (575-591), 2016.
[8] Housila P. Singh and Vishal Mehta, “Improved Estimation of Scale Parameter of Morgenstern Type Bivariate Uniform Distribution Using Ranked Set Sampling”, Communications in Statistics- Theory and Methods, Volum-45, Issue-5 Page No (1466-1476), 2016.
[9] Housila P. Singh and Vishal Mehta, “A Class of Shrinkage Estimators of Scale Parameter of Uniform Distribution Based on K- Record Values”, National Academy Science Letters, Volume-39, Issue-3, Page No (221-227), 2016.
[10] Housula P. Singh and Vishal Mehta,”Improved estimation of the scale parameter for log-logistic distribution using balanced ranked set sampling”, STATISTICS IN TRANSITION-New Series (Accepted), 2016.
[11] J. R. Thompson, “Some shrinkage technique for estimating the mean”, Journal of the American Statistical Association, Volum-63, Issue-321, Page No (113-122), 1968.
[12] J. S. Mehta and R. Srinivasan, “Estimation of the mean by shrinkage to a point”, Journal of the American Statistical Association, Volume- 66, Page No (86-90), 1971.
[13] K. N. Chandler, “The distribution and frequency of record values”, Journal of Royal Statistical Society, Series B, Volum-14, Page No (220-228), 1952.
[14] M. Ahsanullah,”Record Values- Theory and applications”, University press of America, Lanham, MaryIand, USA, Page No (224-232), 2004, ISBN: 978-0-7618-2794-8.
[15] M. Chacko and M. Shy Mary,”Estimation and prediction based on K-record values from normal distribution”, STATISTICA, Volum-73, Issue-4, Page No (505-516), 2013.
[16] N. Balakrishnan and A. C. Cohen, “Order Statistics and Inference: Estimation Method”, Academic Press, San Diego, 1991, ISBN: 978-0120769483.
[17] N. Glick, ”Breaking records and breaking boards”, American Mathematical Monthly, Volume- 85, Page No (2-26), 1978.
[18] V. Nevzorov, “Records: Mathematical Theory. Translation of Mathematical Monographs”, American Mathematical Society, 194, Providence, Rhode IsIand, 2001, ISBN: 978-0-8218-1945-6.
[19] Vishal Mehta and Housila P. Singh, ”Shrinkage Estimators of Parameters of Morgenstern Type Bivariate Logistic Distribution Using Ranked Set Sampling”, Journal of Basic and Applied Engineering Research (JBAER), Volium-1, Issue-13, Page No. (1-6), 2014.
[20] Vishal Mehta and Housila P. Singh, “Minimum Mean Square Error Estimation of Parameters in Bivariate Normal Distribution Using Concomitants of Record Values”, Statistics and Informatics in Agricultural Research, Excel India Publishers, 91A, Ground Floor, Pratik Market, Munirka, New Delhi, India. Page No (162-174), 2015, ISBN: 978-93-84869-98-4.
[21] Vishal Mehta and Housila P. Singh, “Search for Better Estimators Based on k-Record Values from Normal Distribution When Apriori Information is Known”, Proceeding of the 13th National Conference on Recent Trends in Mathematical and Computational Sciences (NCRTMCS-2015), University Department of Statistics and Computer Applications, T. M. Bhagalpur University, Bhagalpur, Bihar, India., 2015.
[22] Vishal Mehta, “Estimation in Morgenstern Type Bivariate Exponential Distribution with Known Coefficient of Variation by Ranked Set Sampling”, Proceeding of the “30th M. P. Young Scientist Congress” (MPYSC-2015), M. P. Council of Science and Technology, Vigyan Bhawan, Nehru Nagar, Bhopal, Madhya Pradesh, India, 2015.
[23] Vishal Mehta, ”Minimum Mean Squared Error Estimators of a Parameter of Morgenstern Type Bivariate Exponential Distribution Using Ranked Set Sampling”, Proceeding of the “31th M. P. Young Scientist Congress” (MPYSC-2016), M. P. Council of Science and Technology, Vigyan Bhawan, Nehru Nagar, Bhopal, Madhya Pradesh, India, 2016.
[24] W. Dziubdziela and B. Kopocinski, ”Limiting properties of the K-th record values”, Zastosowania Matematyki, Volum-15, Page No (187-190), 1976.

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