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http://dx.doi.org/10.14317/jami.2017.477

RELATIONS OF DAGUM DISTRIBUTION BASED ON DUAL GENERALIZED ORDER STATISTICS  

KUMAR, DEVENDRA (Department of Statistics, Central University of Haryana)
Publication Information
Journal of applied mathematics & informatics / v.35, no.5_6, 2017 , pp. 477-493 More about this Journal
Abstract
The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and lower records are deduced from the relations derived and some computational works are also carried out. Further, a characterizing result of this distribution on using the conditional moment of the dual generalized order statistics is discussed. These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, skewness and kurtosis of order statistics and record values of the Dagum distribution.
Keywords
Exact moments; recurrence relation; dual generalized order statistics; order statistics; lower records; Dagum distribution and characterization;
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1 M. Ahsanullah, A characterization of the uniform distribution by dual generalized order statistics, Comm. Statist. Theory Methods 33 (2004), 2921-2928.   DOI
2 M. Ahsanullah, On lower generalized order statistics and a characterization of power function distribution, Stat. Methods 7 (2005), 16-28.
3 E.K. Al-Hussaini, A.A. Ahmad and M.A. Al-Kashif, Recurrence relations for moment and conditional moment generating functions of generalized order statistics, Metrika 61 (2005), 199-220.   DOI
4 M. Burkschat, E. Cramer, E. and U. Kamps, Dual generalized order statistics, Metron LXI (2003), 13-26.
5 C. Daguam, A new model of personal income distribution: Specification and estimation, Econ. Appl. XXX (1977), 413-436.
6 U. Kamps, A concept of generalized order statistics, B.G. Teubner Stuttgart, (1995).
7 R.U. Khan and D. Kumar, On moments of generalized order statistics from exponentiated Pareto distribution and its characterization, Appl. Math. Sci. (Ruse) 4 (2010), 2711-2722.
8 C. Kleiber and S. Kotz, Statistical Size Distribution in Economics and Actuarial Sciences, John Wiley & Sons, Inc., Hoboken, NJ., (2003).
9 C. Kleiber , A guide to the Dagum distribution, in Modeling Income Distributions and Lorenz Curves Series: Economic Studies in Inequality, Social Exclusion and Well-Being, 5, C. Duangkamon, ed.,, Springer, NewYork, NY., (2008).
10 D. Kumar, Lower Generalized Order Statistics Based On Inverse Burr Distribution, American Journal of Mathematical and Management Sciences 35 (2015a), 15-35.
11 D. Kumar, Exact moments of generalized order statistics from type II exponentiated loglogistic distribution, Hacettepe Journal of Mathematics and Statistics 44 (2015b), 715-733.
12 D. Kumar, kth lower record values from of Dagum distribution, Discussiones Mathematicae Probability and Statistics 36 (2016), 25-41.   DOI
13 A.K. Mbah and M. Ahsanullah, Some characterization of the power function distribution based on lower generalized order statistics, Pakistan J. Statist. 23 (2007), 139-146.
14 P. Pawlas and D. Szynal, Recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution, Demonstratio Math. XXXIV (2001), 353-358.
15 S.M. Ruiz, An algebraic identity leading to Wilson's theorem, Math. Gaz. 80 (1996), 579-582.   DOI
16 F. Dommaa, S. Giordanoa and M. Zengab , Maximum likelihood estimation in Dagum distribution with censored samples, Journal of Applied Statistics 38 (2011), 2971-2985.   DOI
17 B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics, John Wiley, New York, (1992).
18 H.A. David and H.N. Nagaraja, Order Statistics, third edition, John Wiley, New York, (2003).