DMPS

Article in volume

Discussiones Mathematicae Probability and Statistics 20(2) (2000) 223-231
DOI: https://doi.org/10.7151/dmps.1013

RECURRENCE RELATIONS FOR SINGLE AND PRODUCT MOMENTS OF k-th LOWER RECORD VALUES FROM THE INVERSE DISTRIBUTIONS OF PARETO'S TYPE AND CHARACTERIZATIONS

Piotr Pawlas and Dominik Szynal

Institute of Mathematics, Maria Curie-Skłodowska University
M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland
e-mail: ppawlas@golem.umcs.lublin.pl
e-mail: szynal@golem.umcs.lublin.pl

Abstract

We give recurrence relations for single and product moments of k-th lower record values from the inverse Pareto, inverse generalized Pareto and inverse Burr distributions. We present also characterization conditions for these distributions.

Keywords and phrases: sample, order statistics, k-th lower record values, moments, product moments, inverse distributions.

1999 Mathematics Subject Classiffication: 62E10, 60E99.

References

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S.A. Klugman, H.H. Panjer and G.E. Willmot, Loss Models, From Data to Decisions, John Wiley & Sons, Inc., 1998.

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G.D. Lin, On a moment problem, Tôhoku Math. Journal 38 (1986), 595-598.

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P. Pawlas and D. Szynal, Relations for single and product moments of k-th record values from exponential and Gumbel distribution, J. Appl. Statist. Sc. 7 (1) (1998), 53-62.

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P. Pawlas and D. Szynal, Recurrence relations for single and product moments of k-th record values from Pareto, generalized Pareto and Burr distributions, Commun. Statist.-Theory Meth. 28 (7) (1999), 1699-1709.

Received 10 March 2000
Revised 6 April 2000