Best Linear Unbiased Estimation and Prediction of Record Values Based on Kumaraswamy Distributed Data

  • Ramy Aldallal Department of accounting, College of Business Administration in Hawtat bani Tamim, Prince Sattam Bin Abdulaziz University, Saudi Arabia
Keywords: upper record values, Kumaraswamy distribution, best linear unbiased estimation, best linear unbiased prediction, moments and product moments.


To predict a future upper record value based on Kumaraswamy distributed data, an explicit expression for single and product moments has been established along with some enhanced expressions that makes the applying process on mathematical softwares easier. The best linear unbiased estimator approach for estimating the parameters and the prediction of future record values have been considered and some important tables have been created to help in the calculation processes. Two illustrative examples based on a simulation study and a real-life data are provided to assess the performance of the introduced results.


J. Ahmadi. Record values, theory and applications. Mashhad,, Iran: Ferdowsi University of Mashhad. Ph. D Thesis, 2000.

M. Ahsanullah. Record statistics, nova sci. Publ., New York, 1995.

B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja. Records, volume 768. John Wiley and Sons, 1998.

N. Balakrishnan and A. C. Cohen. Order statistics and inference: estimation methods. Academic Press, San Diego, 1991.

H. Barakat, E. Nigm, and R. Aldallal. Exact prediction intervals for future current records and record range from any continuous distribution. SORT, 38(2):251–270, 2014.

M. Chacko and M. Shy Mary. Estimation and prediction based on k-record values from normal distribution. Statistica, 73(4):505–516, 2013.

M. Chacko and M. Shy Mary. Estimation and prediction based on k-record values from logistic distribution. Calcutta Statistical Association Bulletin, 66(3-4):137–160, 2014.

K. N. Chandler. The distribution and frequency of record values. Journal of the Royal Statistical Society: Series B (Methodological), 14(2):220–228, 1952.

G. M. Cordeiro, E. M. Ortega, and S. Nadarajah. The kumaraswamy weibull distribution with application to failure data. Journal of the Franklin Institute, 347(8):1399–1429, 2010.

W. Feller. An introduction to probability theory and its applications, vol 2. John Wiley and Sons, 1966.

A. S. Goldberger. Best linear unbiased prediction in the generalized linear regression model. Journal of the American Statistical Association, 57(298):369–375, 1962.

S. Gulati and W. J. Padgett. Smooth nonparametric estimation of thedistribution and density functions from record-breaking data. Communications in Statistics-Theory and Methods, 23(5):1259–1274, 1994.

M. C. Jones. Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Statistical Method-ology, 6(1):70–81, 2009.

F. Kızılaslan and M. Nadar. Estimation and prediction of the kumaraswamy distribution based on record values and inter-record times. Journal of Statistical Computation and Simulation, 86(12):2471–2493, 2016.

P. Kumaraswamy. A generalized probability density function for double-bounded random processes. Journal of Hydrol-ogy, 46(1-2):79–88, 1980.

P. Kumaraswamy, A. Seifi, and J. Vlach. Probabilistic design of systems with general distributions of parameters. International journal of circuit theory and applications, 29(6):527–536, 2001.

A. J. Lemonte, W. Barreto-Souza, and G. M. Cordeiro. The exponentiated kumaraswamy distribution and its log-transform. Brazilian Journal of Probability and Statistics, 27(1):31–53, 2013.

M. Nadar, A. Papadopoulos, and F. Kızılaslan. Statistical analysis for kumaraswamy’s distribution based on record data. Statistical Papers, 54(2):355–369, 2013.

S. Nadarajah. On the distribution of kumaraswamy. JHyd, 348(3):568–569, 2008.

V. B. Nevzorov. Records: mathematical theory. American Mathematical Soc., 2001.

M. Z. Raqab. Inferences for generalized exponential distribution based on record statistics. Journal of statistical planning and inference, 104(2):339–350, 2002.

M. Z. Raqab, J. Ahmadi, and M. Doostparast. Statistical inference based on record data from pareto model. Statistics, 41(2):105–118, 2007.

L. Wang. Inference for the kumaraswamy distribution under k-record values. Journal of Computational and Applied Mathematics, 321:246–260, 2017.

How to Cite
Aldallal, R. (2022). Best Linear Unbiased Estimation and Prediction of Record Values Based on Kumaraswamy Distributed Data. Statistics, Optimization & Information Computing, 10(4), 1250-1266.
Research Articles