Acta Scientific Computer Sciences

Review Article Volume 4 Issue 3

Shrinkage Estimation of Strength Reliability for Geometric Distribution Using Record Values

Glifin Francis1, Anjana EJ2 and ES Jeevanand3*

1Department of Statistics, Nirmala College, Muvatupuzha, Kerala, India
2Department of Mathematics, Ramanujan School of Mathematics, Pondicherry University, Pondicherry, India
3Department of Mathematics, U.C. College, Aluva, Kerala, India

*Corresponding Author: ES Jeevanand, Department of Mathematics, U.C. College, Aluva, Kerala, India.

Received: February 11, 2022; Published: March 15, 2022


In this paper we obtain the shrinkage estimate of R= P(X≤Y) when X the stress and Y the strength are independent geometric variable and the sample on Y the strength is upper records.

Keywords: Shrinkage; Geometric Distribution; Strength


  1. Ashanullah M. “Record Statistics”. Nova Science Publishers, New York (1995).
  2. Arnold BC., et al. Records, John Wiley and Sons, New York (1998).
  3. Chandler K N. “The distribution and frequency of record values”. Journal of the Royal statistical Society, Series B 14 (1952): 220-228.
  4. Dhanya M and Jeevavand E S. “Stress-Strength Reliability of Power Function Distribution based on Records”. Journal of Statistics Applications and Probability 1 (2018): 39-48.
  5. Efron B. “The Jackknife, the Bootstrap and Other Resembling Plans”. SIAM, Philadelphia (1982).
  6. Galambose J. “The Asymptotic Theory of Extreme Order Statistics”. 2nd Edition, Krieger, Florida (1987).
  7. Glick N. “Breaking records and breaking boards”. American Mathematical Monthly 85 (1978): 2-25.
  8. Glifin Francis and Anjana E J. “Estimation of Stress Strength Reliability for Geometric distribution using record values”. Journal of Information Storage and Processing System 20-1 (2021): 175-181.
  9. Gouet Raúl., et al. “Statistical inference for the geometric distribution based on -records”. Computational Statistics and Data Analysis 78 (2014): 21-32.
  10. Gulati S and Padgett W J. “Parametric and Nonparametric Inference from Record Breaking Data”. Springer-Verlag, New York (2003).
  11. Hameed B A., et al. “On Estimation of P (Y1<X<Y2) in Cased Inverse Kumaraswamy Distribution”. Iraqi Journal of Science (2020): 845-853.
  12. Jeevanand E S. "Estimation of reliability under stress-strength model for the geometric distribution in presence of spurious observations". In Statistical Methods for Quality and Reliability: Proceedings of the International Conference on Quality improvement through Statistical Methods. Edited by N. Unnikrishnan Nair and P.G.Sanakran, 1998, 71-81, Educational Publishers, Ernakulam, India (1998).
  13. Khan MJS and Khatoon B. “Statistical inferences of R=P (X<Y) for Exponential Distribution based on Generalized Order Statistics”. Annals of Data Science3 (2020): 525-545.
  14. Madhi Doostparast and Ahamdi J. “Statistical Analysis for geometric distribution based on records”. Computer and Mathematics with Application6-7 (2006): 905-916.
  15. Maiti SS. “Estimation of P (X<Y) in geometric case”. Journal of the Indian Statistical Association2 (1995): 87-91.
  16. Maiti S and Sudhir Murmu. “Bayesian estimation on reliability in two parameter geometric distribution”. Journal of Reliability and Statistical Studies2 (2015): 41-58.
  17. Maiti S., et al. “Estimation of Reliability in the Two-Parameter Geometric Distribution” (2015).
  18. Mathachan Pathiyil and Jeevanand ES. “Reliability measures of geometric distribution by least square procedures”. Recent Advances in Statistical Theory and Applications 1 (2005): 117-125.
  19. Mathachan Pathiyil and Jeevanand ES. “Estimation of the Residual Entropy Function of the Geometric Distribution Using Record Values”. in the Proceedings of the National Workshop on Bayesian Statistics and MCMC Methods using BUGS and R, St. Thomas College, Pala, 26-30, July, (2009).
  20. Mathachan Pathiyil., et al. “On the estimation of the parameter of geometric distribution using record values”. Some Recent Innovation in Statistics (2008): 83-92.
  21. Mathachan Pathiyil Johny Scaria., et al. “Record values from geometric distribution and associated Inference”. STARS2 (2008): 163-174.
  22. McLntyre, G. A. “A method for unbiased selective sampling, using ranked sets”. Australian Journal of Agricultural Research90 (1952): 385-390.
  23. Mehta J S and Srinivasan R. “Estimation of the Mean by shrinkage to a Point”. JASA 66 (1971): 86-90.
  24. Mohamed M O. “Inference for reliability and Stress-Strength for Geometric distribution”. Sylwan 2 (2015): 281-289.
  25. Mohamed M O. “Estimation of R for geometric distribution under lower record values”. Journal of Applied Research and Technology 18 (2020): 368-375.
  26. Nagaraja H N. “Record values and related statistics-a review”. Communications in Statistics-Theory and Methods 17 (1988): 2223-2231.
  27. Nevzorov V B. “Records”. Theory of Probability and Applications 32 (1987): 201-228.
  28. Soliman A A., et al. “Reliability Estimation in Stress-Strength models: an MCMC approach”. Statistics 4 (2013): 715-728.
  29. Wasserman L. “All of statistics: a concise course in statistical inference”. Springer, New York (2003).
  30. Wenbo Yu and Jinyun Xie. “Bayesian Estimation of Reliability of Geometric Distribution under Different Loss Functions”. AMSE JOURNALS-2016-Series: Advances A1 (2016): 172-118.


Citation: ES Jeevanand., et al. “Shrinkage Estimation of Strength Reliability for Geometric Distribution Using Record Values". Acta Scientific Computer Sciences 4.3 (2022): 26-30.


Copyright: © 2022 ES Jeevanand., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Acceptance rate35%
Acceptance to publication20-30 days

Indexed In

News and Events

  • Certification for Review
    Acta Scientific certifies the Editors/reviewers for their review done towards the assigned articles of the respective journals.
  • Submission Timeline for Upcoming Issue
    The last date for submission of articles for regular Issues is July 10, 2022.
  • Publication Certificate
    Authors will be issued a "Publication Certificate" as a mark of appreciation for publishing their work.
  • Best Article of the Issue
    The Editors will elect one Best Article after each issue release. The authors of this article will be provided with a certificate of “Best Article of the Issue”.
  • Welcoming Article Submission
    Acta Scientific delightfully welcomes active researchers for submission of articles towards the upcoming issue of respective journals.
  • Contact US