k-th rekord values from Dagum distribution and characterization

• Autorzy: Devendra Kumar
• Języki publikacji: EN

Abstrakty

EN

In this study, we gave some new explicit expressions and recurrence relations satisfied by single and product moments of k-th lower record values from Dagum distribution. Next we show that the result for the record values from the Dagum distribution can be derived from our result as special case. Further, using a recurrence relation for single moments and conditional expectation of record values we obtain characterization of Dagum distribution. In addition, we use the established explicit expression of single moment to compute the mean, variance, coefficient of skewness and coefficient of kurtosis. Finally, we suggest two applications.

Słowa kluczowe

EN

sample; order statistics; lower record values; single moments; product moments; recurrence relations; Dagum distribution; characterization

Kategorie tematyczne

• 62E10: Characterization and structure theory
• 62G30: Order statistics; empirical distribution functions
• 62G99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2016
• Tom: 36
• Numer: 1-2
• Strony: 25-41

Daty

wydano

2016

otrzymano

2015-10-16

otrzymano

2016-02-12

Twórcy

autor

Devendra Kumar

• Department of Statistics, Amity Institute of Applied Sciences, Amity University Noida-201 303, India

Bibliografia

• [1] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics (John Wiley, New York, 1992).
• [2] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, Records (John Wiley, New York, 1998).
• [3] C. Dagum, A new model of personal income distribution: Specification and estimation, Econ. Appl. XXX (1977), 413-436.
• [4] C. Kleiber and S. Kotz, Statistical Size Distribution in Economics and Actuarial Sciences (John Wiley & Sons, Inc., Hoboken, NJ, 2003).
• [5] 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 (Springer, New York, NY, 2008).
• [6] D. Kumar and M.I. Khan, Recurrence relations for moments of kth record values from generalized beta II distribution and a characterization, Seluk Journal of Applied Mathematics 13 (2012), 75-82.
• [7] D. Kumar, Explicit Expressions and statistical inference of generalized Rayleigh distribution based on lower record values, Math. Meth. Stat. 24 (2015), 225-241.
• [8] D. Kumar, N. Jain and S. Gupta, The type I generalized half logistic distribution based on upper record values, J. Probab. Stat. 2015 (2015). doi: 01-11
• [9] G.D. Lin, On a moment problem, Tohoku Math. J. 38 (1986), 595-598.
• [10] J. Saran and S.K. Singh, Recurrence relations for single and product moments of kth record values from linear exponential distribution and a characterization, Asian J. Math. Stat. 1 (2008), 159-164.
• [11] K.S. Sultan and M.E. Moshref, Record values from generalized Pareto distribution and associated inference, Metrika 51 (2000), 105-116.
• [12] K.N. Chandler, The distribution and frequency of record values, J. Roy. Statist. Soc., Ser. B 14 (1952), 220-228.
• [13] M. Ahsanullah, Record Statistics (Nova Science Publishers, New York, 1995).
• [14] N. Balakrishnan and A.C. Cohan, Order statistics and inference: estimation methods (Boston, MA, Academic Press, 1991).
• [15] N. Balakrishnan and M. Ahsanullah, Recurrence relations for single and product moments of record values from generalized Pareto distribution, Comm. Statist. Theory and Methods 23 (1994), 2841-28526.
• [16] N. Balakrishnan and M. Ahsanullah, Relations for single and product moments of record values from Lomax distribution, Sankhyā Ser. B 56 (1994), 140-146.
• [17] N. Balakrishnan and M. Ahsanullah, Relations for single and product moments of record values from exponential distribution, J. Appl. Statist. Sci. 2 (1995), 73-87.
• [18] N. Balakrishnan, P.S. Chan and M. Ahsanullah, Recurrence relations for moments of record values from generalized extreme value distribution, Comm. Statist. Theory and Methods 22 (1993), 1471-1482.
• [19] P. Pawlas and D. Szynal, Relations for single and product moments of kth record values from exponential and Gumbel distributions, J. Appl. Statist. Sci. 7 (1998), 53-61.
• [20] P. Pawlas and D. Szynal, Recurrence relations for single and product moments of kth record values from weibull distribution and a characterization, J. Appl. Statist. Sci. 10 (2000), 17-25.
• [21] S.I. Resnick, Record values and related statistics, Ann. Probab. 2 (1973), 650-662.
• [22] U. Kamps, Characterizations of distributions by recurrence relations and identities for moments of order statistics, in: N. Balakrishnan, and C.R. Rao, Handbook of Statistics 16 Order Statistics: Theory & Methods, Alavi, Lick and Schwenk (Ed(s)), (North-Holland, Amsterdam, 1998), 291-311.
• [23] W. Feller, An introduction to probability theory and its applications (John Wiley & New York, 1966).
• [24] Z. Grudzień and D. Szynal, Characterization of uniform and exponential distributions via moments of kth record values with random indices, J. Appl. Statist. Sci. 5 (1997), 259-266.

Identyfikatory

DOI

10.7151/dmps.1183