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• Open Access   Article

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

  Vishal Mehta

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.1 , pp.1-5, Feb-2017

  Abstract

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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.
  

  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

• Open Access   Article

  Numerical Study of a Steady State Two Dimensions Heat equation using TDMA Technique

  Arti Kaushik

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.1 , pp.6-11, Feb-2017

  Abstract

  Full-Text HTML

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  Citation

  Abstract
  In this paper, a steady 2-D heat equation was solved numerically using TDMA technique. A steady state two dimensional heat flow is governed by Laplace Equation. Using TDMA technique numerical solution for Laplace equation (heat equation) with constant thermal conductivity has been obtained. Finite volume method is used to obtain system of linear algebraic equations for TDMA technique. The numerical solution obtained is compared with the solution obtained by using Gauss Seidal method. The significant finding of this study is to establish TDMA technique is very efficient for two dimensional problems. A very good agreement between TDMA and Gauss Seidal solutions has also been observed.

  Key-Words / Index Term
  Finite volume method, Heat equation, Laplace equation, Steady state, TDMA technique.

  References
  [1]. Parag V. Patil and J. S. V. R. Krishna Prasad, “Numerical Solution for Two Dimensional Laplace Equation with Dirichlet Boundary Conditions”, International Organization of Scientific Research- Journal of Mathematics, Volume- 6, Issue- 4, Page no.(66-75), May 2013.
  [2]. J. S. V. R. Krishna Prasad and Parag V. Patil, “Finite Volume Numerical Grid Technique for Solving One and Two Dimensional Heat Flow Problems”, Research Journal of Mathematical and Statistical Sciences ,Volume-2, Issue-8, Page no.(4-9), August 2014.
  [3]. Mohammed Hasnat, Nourddine Kaid, Mohammed Bensafi, Abdellah Belkacem , “A numerical Technique Finite Volume Method for Solving Diffusion 2D Problem”, The International Journal Of Engineering And Science, Volume- 4,Issue- 10,Page no.(35-41),October 2015.
  [4] J. D. Anderson,”Computational Fluid Dynamics: The Basics with Applications”, McGraw-Hill Publications, First(Ist) edition, ISBN-0070016852, April 1995.
  [5] H.K. Versteeg, W. Malalsekra, “An Introduction to Computational Fluid Dynamics: The Finite Volume Method”, Prentice Hall, Second(2nd) Edition, ISBN- 0131274988, February 2007.
  [6] Lars Davidson, Peter Hedberg,” Mathematical derivation of a finite volume formulation for laminar flow in complex geometries”, International Journal for Numerical Methods in Fluids , Volume-9 ,Issue-5, Page no.(531-540) ,May 1989.
  [7] M.C. Melaaen, “Calculation of fluid flows with staggered and non staggered curvilinear non orthogonal grids-a comparison”, Numerical heat transfer, Part b: fundamentals, Volume-21, Issue-1, Page no.(21-39), January 1992.
  [8] Bengt Sundén,” Computational Fluid Dynamics in Research and Design of Heat Exchangers”, Heat Transfer Engineering , Volume-28,Issue-11, Page no.(898-910), November 2007.
  [9] T. J. Craft, S. E. Gant , H. Iacovides & B. E. Launder, “A new wall function strategy for complex turbulent flows”, Numerical Heat Transfer, Part B: Fundamentals, Volume-45,Issue-4, Page no.(301-318), 2004.
  [10] Parag V. Patil, J. S. V. R. Krishna Prasad, “The unsteady state finite volume numerical grid technique for multidimensional problems”, Int J. Adv. Appl. Math. and Mech, Volume-. 2, Issue-2, Page no. (78-87),December 2014.
  [11] J. S. V. R. Krishna Prasad and Parag V. Patil , “Finite Volume Numerical Grid Technique for Multidimensional Problems”, International Journal of Science and Research , Volume-3, Issue-7, Page no. (518-523), July 2014.
  [12] Bengt Sunden, “Computational connective and conductive heat transfer”, Advanced Computational Methods in Heat Transfer VI, Volume- 27, 2000, WIT Press. ISBN 1-85312-818-X.
  

  Citation
  Arti Kaushik, "Numerical Study of a Steady State Two Dimensions Heat equation using TDMA Technique," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.1, pp.6-11, 2017