Skip to main content
SpringerLink
Log in

Shrinkage estimation of θα in gamma density G(1/θ, p) using prior information

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

Shrinkage estimation in the gamma density using prior information is valuable in various fields, including finance, healthcare, and environmental science, where accurate parameter estimation is essential for decision-making and modeling. This manuscript considers the problem of estimation of \(\theta^{\alpha }\) in Gamma density G(1/θ, p) when the prior estimate or guessed value of the parameter \(\theta^{\alpha }\) is available in the form of point estimate \(\theta_{0}^{\alpha }\). Some families of estimators of \(\theta^{\alpha }\) are defined with its properties. Estimators developed by other authors are identified as particular members of the suggested families of shrinkage estimators. In particular, we have discussed the properties of the suggested families of estimators in an exponential distribution with known coefficient of variation. Numerical illustrations are also given in order to judge the merits of the proposed families of estimators over others.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

Sharing of data is not applicable to this article, as no datasets were generated or analyzed during the present study.

Code availability

Not applicable.

References

  1. Segal MR, Salamon H, Small PM (2000) Comparing DNA fingerprints of infectious organisms. Stat Sci 15:27–45

    Google Scholar 

  2. Wein LM, Baveja M (2005) Using fingerprint image quality to improve the identification performance of the U.S. visitor and immigrant status indicator technology program. Proc Natl Acad Sci USA 102:7772–7775

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  3. Simpson J (1972) Use of the gamma distribution in single-cloud rainfall analysis. Mon Weather Rev 100:309–312

    Article  ADS  Google Scholar 

  4. Askoy H (2000) Use of gamma distribution in hydrological analysis. Turk J Eng Environ Sci 24:419–428

    Google Scholar 

  5. Bhunya PK, Berndtsson R, Ojha CSP, Mishra SK (2007) Suitability of gamma, chi-square, Weibull, and beta distributions as synthetic unit hydrographs. J Hydrol 334:28–38

    Article  Google Scholar 

  6. Martin R (2002) Speech enhancement using MMSE short time spectral estimation with gamma distributed speech priors. In: Proceedings of the IEEE international conference on acoustics, speech and signal processing, Orlando, FL, pp 253–256

  7. Kim C, Stern RM (2008) Robust signal-to-noise ratio estimation based on waveform amplitude distribution analysis. In: Proceedings of the Interspeech 2008 conference, Brisbane, Australia, pp 2598–2601

  8. Chen P, Ye ZS (2016) Estimation of field reliability based on aggregate lifetime data. Technometrics 59(1):115–125

    Article  MathSciNet  Google Scholar 

  9. Thompson JR (1968) Some shrinkage techniques for estimating the mean. J Am Stat Assoc 63(321):113–123

    MathSciNet  Google Scholar 

  10. Khan AH, Yaqub M, Parvez S (1981) Estimation of in gamma density. Aligarh J Stat 1(2):121–132

    MathSciNet  Google Scholar 

  11. Goodman LA (1953) A simple method for improving some estimators. Ann Math Stat 22:114–117

    Article  MathSciNet  Google Scholar 

  12. Karlin S (1958) Admissibility for estimation with quadratic loss. Ann Math Stat 24:114–117

    MathSciNet  Google Scholar 

  13. El-Sayyad GM (1967) Estimation of the parameter of an exponential distribution. J R Soc Ser B (Stat Methodol) 29:525–532

    MathSciNet  Google Scholar 

  14. Singh HP (1988) Estimation of common parameter in k gamma distribution. Gujrat Stat Rev 15(1):45–48

    MathSciNet  Google Scholar 

  15. Pandey BN, Singh BP (1978) On estimation of r-th power of scale in exponential distribution from complete and censored samples. Prog Math 12(1–2):51–57

    MathSciNet  Google Scholar 

  16. Pandey BN, Singh J (1977) A note on estimation of variance in exponential density. Sankhya B 39:294–298

    MathSciNet  Google Scholar 

  17. Sathe YS (1979) A further note on estimation of variance in exponential density. Sankhya B 41:122–123

    MathSciNet  Google Scholar 

  18. Searls DT (1964) The utilization of a known coefficient of variation in the estimation procedure. J Am Stat Assoc 59:1225–1226

    Article  Google Scholar 

  19. Davis RL, Arnold AC (1970) An efficient preliminary test estimator for variance of a normal population when mean is unknown. Biometrika 57:674–677

    Google Scholar 

  20. Thompson JR (1968) Accuracy borrowing in the estimation of the mean by shrinkage to an interval to an interval. J Am Stat Assoc 63(323):953–963

    Google Scholar 

  21. Mehta JS, Srinivasan R (1971) Estimation of the mean by shrinkage to a point. J Am Stat Assoc 66:86–90

    Article  Google Scholar 

  22. Pandey BN (1983) shrinkage estimation of the exponential scale parameter. IEEE Trans Reliab 32:203–205

    Article  Google Scholar 

  23. Pandey BN, Srivastava R (1985) On shrinkage estimation of the exponential scale parameter. IEEE Trans Reliab 34:224–226

    Article  Google Scholar 

  24. Jani PN (1991) A class of shrinkage estimators for the scale parameter of the exponential distribution. IEEE Trans Reliab 40:68–70

    Article  ADS  Google Scholar 

  25. Kourouklis S (1994) Estimation in the 2-parameter exponential distribution with prior information. IEEE Trans Reliab 43(3):446–450

    Article  Google Scholar 

  26. Singh HP, Gangele RK, Singh R (1993) Some shrinkage estimators for the scale parameter of the exponential distribution. Vikram Math J 13:57–64

    MathSciNet  Google Scholar 

  27. Singh HP, Saxena S, Mathur N (2001) Estimation of exponential scale parameter in failure censored samples by shrinkage towards an interval. Varahmihir J Math Sci 1(1):9–22

    MathSciNet  Google Scholar 

  28. Tracy DS, Singh HP, Raghuvanshi HS (1996) Some shrinkage estimators for the variance of exponential density. Microelectron Reliab 36(5):651–655

    Article  Google Scholar 

  29. Singh HP, Raghuvanshi HS (1996) A new shrinkage estimator for the exponential scale parameter. Microelectron Reliab 36(1):105–107

    Article  Google Scholar 

  30. Saxena S, Singh HP (2004) Estimating various measures in normal population through a single class of estimators. J Korean Stat Soc 33(3):323–337

    MathSciNet  Google Scholar 

  31. Baklizi A (2004) Shrinkage estimation of the common location parameter of several exponentials. Commun Stat Simul Comput 33(2):321–339

    Article  MathSciNet  Google Scholar 

  32. Singh HP, Singh S, Jong-Min K (2012) Some alternative classes of shrinkage estimators for a scale parameter of the exponential distribution. Korean J Appl Stat 25(2):301–309

    Article  Google Scholar 

  33. Zakerzadeh H, Jafari AA, Karimi M (2016) Optimal shrinkage estimations for the parameters of exponential distribution based on record values. Rev Colomb Estadística 39(1):33–44

    Article  MathSciNet  Google Scholar 

  34. Xie X, Kou SC, Brown LD (2016) Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance. Ann Stat 44(2):564–597

    Article  MathSciNet  PubMed  PubMed Central  Google Scholar 

  35. Nasiri P, Nooghabi MJ (2018) On bayesian shrinkage estimator of parameter of exponential distribution with outliers. Punjab Univ J Math 50(2):11–19

    MathSciNet  Google Scholar 

  36. Vishwakarma GK, Gupta S (2022) Shrinkage estimator for scale parameter of gamma distribution. Commun Stat Simul Comput 51(6):3073–3080

    Article  MathSciNet  Google Scholar 

  37. Gupta S, Vishwakarma GK, Elsawah AM (2023) Shrinkage estimation of the location and scale parameters of logistic distribution under record values. Ann Data Sci, https://doi.org/10.1007/s40745-023-00492-2

  38. Vishwakarma GK, Gupta S, Elsawah AM (2023) Shrinkage estimation of location parameter for uniform distribution based on k-record values. Sankhya B 85:405–419

    Article  MathSciNet  Google Scholar 

  39. James W, Stein C (1961) A basic paper on stein type estimators. In: Proceedings of the 4th Berkeley symposium on mathematical statistics, vol 1. University of California Press, Berkeley, pp 361–379

Download references

Acknowledgements

The authors are grateful to the editor-in-chief Prof. S. Kumar and anonymous reviewers for their valuable suggestions which helped in improving the quality of this manuscript.

Funding

There is no specific funding received to support this research.

Author information

Authors and Affiliations

  1. School of Studies in Statistics, Vikram University, Ujjain, 456010, India

    Housila P. Singh & Harshada Joshi

  2. Department of Mathematics & Computing, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, 826004, India

    Gajendra K. Vishwakarma

Authors
  1. Housila P. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harshada Joshi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gajendra K. Vishwakarma
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

HPS conceptualized the study, HJ developed the data analysis methodology, analyzed the data, and drafted this manuscript. GKV reviewed the draft manuscript and provided technical inputs to HPS to finalize the manuscript. All authors contributed equally.

Corresponding author

Correspondence to Harshada Joshi.

Ethics declarations

Competing interests

The authors declare that they have no competing interests.

Ethical approval

This research is an original work of the authors and has not been previously published elsewhere.

Consent to participate

All authors have provided their consent to participate in this research.

Consent for publication

The authors have granted consent for the publication of identifiable details, including figures, graphs, tables, and case studies, in the specified journal.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, H.P., Joshi, H. & Vishwakarma, G.K. Shrinkage estimation of θα in gamma density G(1/θ, p) using prior information. J Eng Math 144, 18 (2024). https://doi.org/10.1007/s10665-023-10329-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10665-023-10329-9

Keywords

Search

Navigation