On Generalized Upper(k)Record Values From Weibull Distribution

Authors

  • Jerin Paul University of Kerala, Trivandrum
  • Poruthiyudian Yageen Thomas University of Kerala, Trivandrum

DOI:

https://doi.org/10.6092/issn.1973-2201/6100

Keywords:

Best Linear Unbiased Estimation, Best Linear Unbiased Predictor, Characterization, Generalized upper(k)record values, Weibull Distribution

Abstract

In this paper we study the generalized upper(k)record values arising from Weibull distribution. Expressions for the moments and product moments of those generalized upper(k)record values  are derived. Some properties of generalized upper(k)record values which characterize the Weibull distribution  have been established. Also some distributional properties of generalized upper(k)record values arising from Weibull distribution are considered and used for suggesting an estimator for the shape parameter of Weibull distribution. The location and scale parameters are estimated using the Best Linear Unbiased Estimation procedure. Prediction of a future record using Best Linear Unbiased Predictor has been studied. A real life data is used to illustrate the results generated in this work.

References

J. ACZEL (1966). Lectures on Functional Equations and Their Applications. Academic Press, New York.

B. C. ARNOLD, N. BALAKRISHNAN, H. N. NAGARAJA (1998). Records. John Wiley and Sons, New York.

N. BALAKRISHNAN, P. S. CHAN (1993). Record values from Rayleigh and Weibull distributions and associated inference. National Institute of Standards and Technology Journal of Research, Special Publication, 866, pp. 41–51.

P. S. CHAN (1993). A statistical study of log-gamma distribution. Ph.D. thesis, McMaster University, Canada.

P. S. CHAN (1998). Interval estimation of location and scale parameters based on record values. Statistics & probability letters, 37, no. 1, pp. 49–58.

K. N. CHANDLER (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society. Series B, 14, pp. 220–228.

A. C. DALLAS (1982). Some results on record values from the exponential and Weibull law. Acta Mathematica Hungarica, 40, no. 3, pp. 307–311.

W. DZIUBDZIELA, B. KOPOCINSKI (1976). Limiting properties of the kth record values. Zastos. Mat., 15, pp. 187–190.

N. GLICK (1978). Breaking records and breaking boards. American Mathematical Monthly, 85, pp. 2–26.

S. GULATI, W. J. PADGETT (2003). Parametric and Nonparametric Inference from Record Breaking Data. 172. Springer-Verlag, New York.

K. S. JOHNSON, N. L., N. BALAKRISHNAN (1994). Continuous univariate distributions, Vol. 1. John Wiley & Sons, New York.

S. MINIMOL, P. Y. THOMAS (2013). On some properties of Makeham distribution using generalized record values and its characterizations. Brazilian Journal of Probability and Statistics, 27, no. 4, pp. 487–501.

S. MINIMOL, P. Y. THOMAS (2014). On characterization of Gompertz distribution by generalized record values. Journal of Statistical Theory and Applications, 13, pp. 38–45.

V. B. NEVZOROV (2001). Records: Mathematical Theory. Translation of Mathematical Monographs, vol. 194. American Mathematical Society, Providence, RI, USA.

J. PAUL, P. Y. THOMAS (2013). On a property of generalized record values arising from exponential distribution. Indian Association for Productivity, Quality and Reliability Transactions, 38, pp. 19–27.

P. PAWLAS, D. SZYNAL (1998). Relations for single and product moment of k-th record values from exponential and Gumbel distribution. J. Appl. Statist. Sci, 7, pp. 53–62.

P. PAWLAS, D. SZYNAL (1999). Recurrence relations for single and product moment of k-th record values from Pareto, generalized Pareto and Burr distributions. Communications in Statistics-Theory Methods, 28, pp. 1699–1709.

H. RINNE (2008). The Weibull Distribution : A Handbook. CRC Press, Taylor & Francis Group, LLC.

E. M. ROBERTS (1979). Review of statistics of extreme values with application to air quality data, part ii: applications. Journal of the Air Pollution Control Association, 29, no. 7, pp. 733–740.

W. WEIBULL (1951). A statistical distribution function of wide applicability. J. Appl. Mech.-Trans. ASME, 18, pp. 293–297.

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Published

2015-09-30

How to Cite

Paul, J., & Thomas, P. Y. (2015). On Generalized Upper(k)Record Values From Weibull Distribution. Statistica, 75(3), 313–330. https://doi.org/10.6092/issn.1973-2201/6100

Issue

Vol. 75 No. 3 (2015)

Section

Articles

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