MC

Current Trends in Science and Technology

an Open Access Publication ISSN: 0976-9730 | 0976-9498

Maths

Bayesian Approximation of Hazard Rate Function of Three Parameter Generalized Compound Rayleigh Distribution Under General Entropy Loss Function.

Parul Yadav
Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur, U.P., India.
Uma Srivastava
Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur, U.P., India
Online First: April 27, 2018
| Google Scholar

Abstract

The Failure process is usually quite complex and is often difficult to understand the physics of underlying process. It is even more difficult to mathematically describe such a process. Consequently a failure distribution is used to provide a statistical summary account of the length of life of a device and choice of distribution is largely an art. The main objective of the paper is to discuss about the use and importance of the Hazard rate function in real world. Then we obtain the Approximate Bayes estimate of the Hazard rate function of, Generalized Compound Rayleigh distribution (re-parameterized) in complete sample case under the squared error loss function and general entropy loss function through the Lindley approximation procedure. We also analyze the sensitivity of Approximate Bayes Estimate of model and presented a numerical study to illustrate the above technique on generated observations. The comparison is done by using R-programming.

  Submitted
Apr 26, 2018
Published
Apr 27, 2018
Abstract Views
66
PDF Downloads
79
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

1. Bain, L.J., & Engelhardt, M.(1991):Statistical analysis of reliability and life testing models :Theory and Methods. New York: M. Dekker. 2. Bhattacharya, S.K. (1967): “Bayesian Approach to Life Testing and Reliability”. J. Amer Statist. Assoc., Vol. 62, pp 48-62. 3. Box,G.E.P and Tiao, G.C. (1973): “Bayesian Inference in Statistical Analysis” Addison Wasley, Reading M.A 4. Burr, I.W. (1942): “Cumulative Frequency Distribution", Annals of Mathematical Statistics, Vol. 13, pp 215-232. 5. Calabria, R. and Pulcini, G. (1994): “An Engineering Approach to Bayes Estimation for the Weibull Distribution”, Microelectronics Reliability, Vol. 34 No-5, pp. 789-802. De Groot (1970): “Optimal Statistical Decisions”McGraw hill, New York . 6. Dey, D.K. and Pei-San Liao Liu (1992): “On Comparison of Estimators in A Generalized Life Model”, Microelectron. Reliab., Vol. 32 No. 1/2, pp 207-221. 7. Dey, D.K., Ghosh, M. and Srinivasan, C. (1987): “Simultaneous Estimation of Parameter under Entropy Loss”, Jour. Statist. Plan and Infer., pp 347-363. 8. Dubey, S., Pradhan, B. and Kundu, D. (2010): “Parameter Estimation of The Generalized Rayleigh Distribution”. 9. George W. Evans; Simulation Using Digital Computers;pp. 60-67. 10. Grohowski, G.;Hausman, W.;Lamberson,L.R. (1976,ASQC) General Motor Corporation, Warren.MI; Wayne State University,Detroit,MI.QICID:5240 October 1976 pp.197-208. 11. Jeffrey, H.(1961):“Theory of Probability” Oxford University Press (3rd ed.) 12. Lindley, D.V. (1980): “Approximate Bayesian Method”. Trab. Esta., Vol. 31, pp 223-237. 13. Mostert, J.J.J.,Roux and Bekker(2000): ‘A Generalized Compond Rayleigh Distribution Using Bayesian Method 29;7, 1419-1433’ 14. Raffia, H. and Schlaifer, R. (1961): “Applied Statistical Decision Theory”, Graduate school of business administration, Harward University, Bostan, MA 15. Satya D. Dubey ;june (1968) https//doi.org/10.1002/nav.3800150205. 16. Sinha, S.K. (1980): “Robustness of Posteriors under Improper Priors in Some Life Testing Models”, J. Indian Statist. Assoc., Vol. 18, pp. 127-144. 17. Sinha, S.K. (1986): “Reliability And Life Testing”, Wiley Eastern Ltd., Delhi, India. 18. Sinha, S.K. and Sloan, J.A. (1988): “Bayesian Estimation of Parameters and Reliability Function Of The 3-Paramters Weibull Distrib.”. IEEE Tra. Rel., V-R-37, pp 364-369. 19. Siddiqui,J. and Weiss,G (1963):Families of Distributions for received power of radio wave,J. Research of the NBS, D. Radio Propagation, 753-762. 20. Soliman, A.A. (2001): “Linex and Quadratic Approximate Bayesian Estimators Applied to Pareto Model”, Communication in Statistics - Simulation Vol. 30, No.1, pp 47-62. 21. Varian, H.R. (1975):”A Bayesian Approach to Real Estate Assessment, in Studies in Bayesian Econometrics and Statistics in Honor of Leonard J.Savage”, S.E.Fienberg and A.Zellner, Eds. pp. 195-208, North-Holland Amsterdam, the Neterlands. 22. Zellner, A. and Giesel, M.S. (1968): “Sensitivity of Control to Uncertainty and Form of Criterion Function in the Future of Statistics”. ed. Donal G. Watts. N Y Academic Press.
Downloads

Downloads

Download data is not yet available.

References

1. Bain, L.J., & Engelhardt, M.(1991):Statistical analysis of reliability and life testing models :Theory and Methods. New York: M. Dekker.
2. Bhattacharya, S.K. (1967): “Bayesian Approach to Life Testing and Reliability”. J. Amer Statist. Assoc., Vol. 62, pp 48-62.
3. Box,G.E.P and Tiao, G.C. (1973): “Bayesian Inference in Statistical Analysis” Addison Wasley, Reading M.A
4. Burr, I.W. (1942): “Cumulative Frequency Distribution", Annals of Mathematical Statistics, Vol. 13, pp 215-232.
5. Calabria, R. and Pulcini, G. (1994): “An Engineering Approach to Bayes Estimation for the Weibull Distribution”, Microelectronics Reliability, Vol. 34 No-5, pp. 789-802. De Groot (1970): “Optimal Statistical Decisions”McGraw hill, New York .
6. Dey, D.K. and Pei-San Liao Liu (1992): “On Comparison of Estimators in A Generalized Life Model”, Microelectron. Reliab., Vol. 32 No. 1/2, pp 207-221.
7. Dey, D.K., Ghosh, M. and Srinivasan, C. (1987): “Simultaneous Estimation of Parameter under Entropy Loss”, Jour. Statist. Plan and Infer., pp 347-363.
8. Dubey, S., Pradhan, B. and Kundu, D. (2010): “Parameter Estimation of The Generalized Rayleigh Distribution”.
9. George W. Evans; Simulation Using Digital Computers;pp. 60-67.
10. Grohowski, G.;Hausman, W.;Lamberson,L.R. (1976,ASQC) General Motor Corporation, Warren.MI; Wayne State University,Detroit,MI.QICID:5240 October 1976 pp.197-208.
11. Jeffrey, H.(1961):“Theory of Probability” Oxford University Press (3rd ed.)
12. Lindley, D.V. (1980): “Approximate Bayesian Method”. Trab. Esta., Vol. 31, pp 223-237.
13. Mostert, J.J.J.,Roux and Bekker(2000): ‘A Generalized Compond Rayleigh Distribution Using Bayesian Method 29;7, 1419-1433’
14. Raffia, H. and Schlaifer, R. (1961): “Applied Statistical Decision Theory”, Graduate school of business administration, Harward University, Bostan, MA
15. Satya D. Dubey ;june (1968) https//doi.org/10.1002/nav.3800150205.
16. Sinha, S.K. (1980): “Robustness of Posteriors under Improper Priors in Some Life Testing Models”, J. Indian Statist. Assoc., Vol. 18, pp. 127-144.
17. Sinha, S.K. (1986): “Reliability And Life Testing”, Wiley Eastern Ltd., Delhi, India.
18. Sinha, S.K. and Sloan, J.A. (1988): “Bayesian Estimation of Parameters and Reliability Function Of The 3-Paramters Weibull Distrib.”. IEEE Tra. Rel., V-R-37, pp 364-369.
19. Siddiqui,J. and Weiss,G (1963):Families of Distributions for received power of radio wave,J. Research of the NBS, D. Radio Propagation, 753-762.
20. Soliman, A.A. (2001): “Linex and Quadratic Approximate Bayesian Estimators Applied to Pareto Model”, Communication in Statistics - Simulation Vol. 30, No.1, pp 47-62.
21. Varian, H.R. (1975):”A Bayesian Approach to Real Estate Assessment, in Studies in Bayesian Econometrics and Statistics in Honor of Leonard J.Savage”, S.E.Fienberg and A.Zellner, Eds. pp. 195-208, North-Holland Amsterdam, the Neterlands.
22. Zellner, A. and Giesel, M.S. (1968): “Sensitivity of Control to Uncertainty and Form of Criterion Function in the Future of Statistics”. ed. Donal G. Watts. N Y Academic Press.
No Supplimentary Material available for this article.

Statistics from Altmetric.com

Statistics from Dimensions.ai

Statistics from PlumX


Related Articles

Related Authors

 



In Google Scholar

In International Journal of Current Trends in Science and Technology

In Google Scholar

 
  • Parul Yadav
  • Uma Srivastava

  • INDEXING AND ABSTRACTING