×

zbMATH — the first resource for mathematics

Recurrence relations for single and product moments of record values from generalized Pareto distribution. (English) Zbl 0850.62118
Summary: In this paper we establish some recurrence relations satisfied by single and product moments of upper record values from the generalized Pareto distribution. It is shown that these relations may be used to obtain all the single and product moments of all record values in a simple recursive manner. We also show that similar results established recently by Balakrishnan and Ahsanullah (1993) for the upper record values from the exponential distribution may be deduced by letting the shape parameter \(\beta\) tend to 0.

MSC:
62-XX Statistics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ahsanullah M., Introduction to Record Values (1988)
[2] Ahsanuuah M., In Order Statistics and Nonparametrics:Theory and Applications pp 47– (1992)
[3] Arnold B.C., Pareto Distributions (1983) · Zbl 1169.62307
[4] Arnold B.C., Lecture Notes in Statistics 53 (1989)
[5] Arnold B.C., A First Course in Order Statistics (1992) · Zbl 0850.62008
[6] Balakrishnan N., J. Appl. Statist. Sc (1993)
[7] DOI: 10.1016/0167-7152(92)90193-9 · Zbl 0752.62012
[8] DOI: 10.1080/03610929308831097 · Zbl 0784.62012
[9] Chandler K.M., J. Roy. Statist. Soc 14 pp 220– (1952)
[10] Feller W., An Introduction to Probability Theory and Its Applications 2 (1966) · Zbl 0138.10207
[11] DOI: 10.2307/2978044 · Zbl 0395.62040
[12] DOI: 10.2307/1269343 · Zbl 0628.62019
[13] DOI: 10.1007/BF00363510 · Zbl 0588.62021
[14] DOI: 10.1080/03610928808829743 · Zbl 04528298
[15] DOI: 10.1137/1132032 · Zbl 0677.62044
[16] DOI: 10.1214/aos/1176343003 · Zbl 0312.62038
[17] Reiss R.D., Approximate Distributions of Order Statistics:With Applications to Nonparametric Statistics (1989) · Zbl 0682.62009
[18] DOI: 10.1214/aop/1176996892 · Zbl 0261.60024
[19] DOI: 10.2307/3212775 · Zbl 0268.60075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.