Empirical Bayes inference for generalized exponential distributions based on records. (English) Zbl 1213.62014
Summary: Record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of the observations. Bayes and empirical Bayes estimators for the unknown parameter of the generalized exponential distribution are derived based on record statistics. These estimates are obtained based on squared error and LINEX loss functions. Prediction bounds for future lower record values are obtained by using Bayes and empirical Bayes techniques. A numerical example is given to illustrate the results.
MSC:
62C12 | Empirical decision procedures; empirical Bayes procedures |
62G32 | Statistics of extreme values; tail inference |
62F10 | Point estimation |
62F15 | Bayesian inference |
62G30 | Order statistics; empirical distribution functions |
65C60 | Computational problems in statistics (MSC2010) |
References:
[1] | Abramowitz M., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (1972) · Zbl 0543.33001 |
[2] | Ahsanullah M., Pakistan J. Statist. 7 pp 53– (1991) |
[3] | Ahsanullah M., Record Statistics (1995) · Zbl 0907.62017 |
[4] | DOI: 10.1017/CBO9780511569647 · doi:10.1017/CBO9780511569647 |
[5] | DOI: 10.1080/02331880210929 · Zbl 0997.62021 · doi:10.1080/02331880210929 |
[6] | Arnold B. C., Records (1998) |
[7] | DOI: 10.1080/03610929008830297 · doi:10.1080/03610929008830297 |
[8] | Calabria R., Commun. Statist. Theor. Meth. 25 pp 285– (1996) |
[9] | Chandler K. N., J. R. Statist. Soc. 14 pp 220– (1952) |
[10] | DOI: 10.1007/BF02480982 · Zbl 0522.62027 · doi:10.1007/BF02480982 |
[11] | DOI: 10.1111/1467-842X.00072 · Zbl 1007.62503 · doi:10.1111/1467-842X.00072 |
[12] | IMSL, Reference Manual (1984) |
[13] | Maritz J. L., 2nd ed., in: Empirical Bayes Methods (1989) |
[14] | DOI: 10.1080/03610928808829743 · doi:10.1080/03610928808829743 |
[15] | DOI: 10.1016/S0378-3758(01)00246-4 · Zbl 0992.62013 · doi:10.1016/S0378-3758(01)00246-4 |
[16] | DOI: 10.1080/00949650108812085 · Zbl 1151.62309 · doi:10.1080/00949650108812085 |
[17] | DOI: 10.1016/0167-7152(92)90091-I · Zbl 0743.62043 · doi:10.1016/0167-7152(92)90091-I |
[18] | DOI: 10.1109/TR.1972.5215977 · doi:10.1109/TR.1972.5215977 |
[19] | Varian H. R., Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage pp 195– (1975) |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.