Statistical analysis for Kumaraswamy’s distribution based on record data
- 667 Downloads
In this paper we review some results that have been derived on record values for some well known probability density functions and based on m records from Kumaraswamy’s distribution we obtain estimators for the two parameters and the future sth record value. These estimates are derived using the maximum likelihood and Bayesian approaches. In the Bayesian approach, the two parameters are assumed to be random variables and estimators for the parameters and for the future sth record value are obtained, when we have observed m past record values, using the well known squared error loss (SEL) function and a linear exponential (LINEX) loss function. The findings are illustrated with actual and computer generated data.
KeywordsKumaraswamy’s distribution Record values Bayes estimator LINEX loss function SE loss function Prediction of future record values
Mathematics Subject Classification (2000)62F15
Unable to display preview. Download preview PDF.
- Ahmadi J (2000) Record values, theory and applications. PhD thesis, Ferdowsi University of Mashhad, Mashhad, IranGoogle Scholar
- Basak P, Balakrishnan N (2003) Maximum likelihood prediction of future record statistic. Mathematical and statistical methods in reliability. In: Lindquist BH, Doksun KA (eds) Series on quality, reliability and engineering statistics, vol 7. World Scientific Publishing, Singapore, pp 159–175Google Scholar
- Canavos GC, Tsokos CP (1971) A study of an ordinary and empirical Bayes approach to reliability estimation in the gamma life testing model. In: Proceedings annual symposium reliability, pp 343–349Google Scholar
- Feller W (1966) An introduction to probability theory and its applications, vol 2, 2nd edn. Wiley, New YorkGoogle Scholar
- Nevzorov V (2001) Records: mathematical theory. Translation of Mathematical Monographs, vol 194. Amer. Math. Soc., ProvidenceGoogle Scholar
- Robbins H (1956) An empirical Bayes approach to statistics. In: Proceedings of the third Berkeley symposium on mathematical statistics and probability, vol 1: contributions to the theory of statisticsGoogle Scholar
- Varian HR (1975) A Bayesian approach to real estate assessment. In: Finberg SE, Zellner A. (eds) Studies in Bayesian econometrics and statistics in honor of Leonard J. Savege. North Holland, Amesterdam, pp 195–208Google Scholar