Browse > Article
http://dx.doi.org/10.14317/jami.2014.007

QUOTIENT MOMENTS OF THE ERLANG-TRUNCATED EXPONENTIAL DISTRIBUTION BASED ON RECORD VALUES AND A CHARACTERIZATION  

Kumar, Devendra (Department of Statistics, Amity Institute of Applied Sciences Amity University)
Publication Information
Journal of applied mathematics & informatics / v.32, no.1_2, 2014 , pp. 7-16 More about this Journal
Abstract
Erlang-truncated exponential distribution is widely used in the field of queuing system and stochastic processes. This family of distribution include exponential distribution. In this paper we establish some exact expression and recurrence relations satisfied by the quotient moments and conditional quotient moments of the upper record values from the Erlang-truncated exponential distribution. Further a characterization of this distribution based on recurrence relations of quotient moments of record values is presented.
Keywords
Record; quotient moments; recurrence relations; Erlang-truncated exponential distribution and characterization;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 A.R. El-Alosey, Random sum of new type of mixture of distribution, Int. J. Statist. Syst. 2 (2007), 49-57.
2 B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A First course in Order Statistics, John Wiley and Sons, New York, 1992.
3 B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, Records, John Wiley, New York, 1998.
4 D. Kumar, Relations for moments of k-th lower record values from exponentiated log-logistic distribution and a characterization, International Journal of Mathematical Archive, 6 (2011), 813-819.
5 D. Kumar, Recurrence relations for moments of record values from generalized beta II distribution and characterization. , Journal of Applied Mathematics and Informatics, (In Press), (2012).
6 D. Kumar and M.I. Khan, Recurrence relations for moments of K-th record values from generalized beta distribution and a characterization, Seluk J. App. Math., 13 (2012), 75-82.
7 I,S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series of Products, Academic Press, New York, 2007.
8 J.S. Hwang and G.D. Lin, On a generalized moments problem II, Proc. Amer. Math. Soc. 91 (1984), 577-580.   DOI   ScienceOn
9 K.N. Chandler, The distribution and frequency of record values, J. Roy. Statist. Soc., Ser B 14 (1952), 220-228.
10 M. Ahsanullah, Record Statistics, Nova Science Publishers, New York, 1995.
11 M.Y. Lee and S.K. Chang, Recurrence relations of quotient moments of the exponential distribution by record values, Honam Mathematical J. 26 (2004), 463-469.   과학기술학회마을
12 M.Y. Lee and S.K. Chang, Recurrence relations of quotient moments of the Pareto dis-tribution by record values, J. Korea Soc. Math. Educ. Ser B: Pure Appl. Math. 11 (2004), 97-102.   과학기술학회마을
13 M.Y. Lee and S.K. Chang, Recurrence relations of quotient moments of the power function distribution by record values, Kangweon-Kyungki Math. J. 12 (2004), 15-22.
14 P. Pawlas and D. Szynal, Relations for single and product moments of k-th record values from exponential and Gumbel distributions, J. Appl. Statist. Sci. 7 (1998), 53-61.
15 P. Pawlas and D. Szynal, Recurrence relations for single and product moments of k-th record values from Pareto, generalized Pareto and Burr distributions, Comm. Statist. Theory Methods, 28 (1999), 1699-1709.   DOI
16 P. Pawlas and D. Szynal, Recurrence relations for single and product moments of k-th record values from Weibull distribution and a characterization, J. Appl. Stats. Sci. 10 (2000), 17-25.
17 S.I. Resnick, Extreme values, regular variation and point processes, Springer-Verlag, New York, 1973.
18 S.K. Chang, Recurrence relations of quotient moments of the Weibull distribution by record values, J. Appl. Math. and Computing 1 (2007), 471-477.
19 U. Kamps, A concept of generalized Order Statistics, J. Statist. Plann. Inference 48 (1995), 1-23.   DOI   ScienceOn
20 U. Kamps, Characterizations of distributions by recurrence relations and identities for moments of order statistics. In: Balakrishnan, N. and Rao, C.R., Handbook of Statistics, Order Statistics: Theory and Methods. North-Holland, Amsterdam 16 (1998), 291-311.
21 V.B. Nevzorov, Records , Theory probab. Appl. 32, (English translation), 1987.
22 W. Dziubdziela and B. Kopocinski, Limiting properties of the k-th record value, . Appl. Math. ,15 (1976), 187-190.
23 W. Feller, An introduction to probability theory and its applications, 2, John Wiley and Sons, New York, 1966.