Record values from a family of J-shaped distributions

Authors

  • Ahmad A. Zghoul The University of Jordan

DOI:

https://doi.org/10.6092/issn.1973-2201/3619

Abstract

A family of J-shaped distributions has applications in life testing modeling. In this paper we study record values from this family of distributions. Based on lower records, recurrence relations and bounds as well as expressions for moments and product moments of record values are obtained, the maximum likelihood estimator of the shape parameter is derived and shown to be consistent, sufficient, complete and UMVU estimator. In addition, an application in reliability is given.

References

M. AHSANULLAH, (1995), Introduction to Record Statistics, NOVA Science Publishers Inc., Hungtington, New York.

B.C. ARNOLD, N. BALAKRISHNAN, H.N. NAGARAJA, (1998), Records, John Wiley and Sons.

K.N. CHANDLER, (1952), The distribution and frequency of record values, “Journal of the Royal Statistical Society”, Series B, 14, pp. 220-228.

I.S. GRADSHTEYN, I. M. RYZHIK, (1980), Table of Integrals, Series, and Products, Academic Press, Orlando, Florida, USA.

J.F. LAWLESS, (1982), Statistical models and methods for lifetime data, John Wiley and Sons.

S. NADARAJAH. S. KOTZ, (2003), Moments of Some J-Shaped Distributions, “Journal of Applied Statistics”, 30(3), pp. 311-317.

H.N. NAGARAJA, (1988), Record Values and Related Statistics- A review, “Communications in Statistics- Theory and Methods ”, 17, pp. 2223-2238.

V.B. NEVZOROV, (1987), Records, “Theory of Probability and Applications”, 32(2), pp. 201-228.

V.B. NEVZOROV, N. BALAKRISHNAN, (1998). A Record of Records, “In Handbook of Statistics- 16: Order Statistics: Theory and Methods”, pp. 515-570, North-Holland, Amsterdam, The Netherlands.

C.W. TOPP, F.C. LEONE, (1955), A family of J-Shaped Frequency Functions, “Jounal of the American Statistical Association”, 50, pp. 209-219.

A.A. ZGHOUL, (2010), Order statistics from a family of J-shaped distributions, to appear in “METRON”, LXVIII, n. 2, pp. 127-136.

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Published

2011-08-30

How to Cite

Zghoul, A. A. (2011). Record values from a family of J-shaped distributions. Statistica, 71(3), 355–365. https://doi.org/10.6092/issn.1973-2201/3619

Issue

Vol. 71 No. 3 (2011)

Section

Articles

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Copyright (c) 2011 Statistica

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