×

Characterization and statistical test using truncated expectations for a class of skew distributions. (English) Zbl 0584.62021

The expectation of left truncated Waring and Pareto distributions is a linear function of the point of truncation. Based on this property, a characterization theorem and statistical tests can be constructed.

MSC:

62E10 Characterization and structure theory of statistical distributions
62G10 Nonparametric hypothesis testing
62F03 Parametric hypothesis testing
Full Text: DOI

References:

[1] Epstein, B.; Josselson, H. H., The Russian World Count, V (1973), Wayne University Press: Wayne University Press Detroit
[2] Feller, W., An introduction to Probability Theory and Its Applications (1957), Wiley: Wiley New York · Zbl 0155.23101
[3] Haitun, S. D., Stationary scientometric distributions. Part III. The role of the Zipf distribution, Scientometrics, 4, 3, 181-194 (1982)
[4] Herdan, G., Type-Token Mathematics (1960), Mouton: Mouton The Hague · Zbl 0163.40904
[5] Herdan, G., Quantitative Linguistics (1964), Butterworths: Butterworths London · Zbl 0143.20905
[6] Irwin, J. O., The place of mathematics in medical and biological statistics, J. Roy. Stat. Soc. A, 126, 1-45 (1963)
[7] Irwin, J. O., The generalized Waring distribution applied to accident theory, J. Roy. Stat. Soc. A, 131, 205-225 (1968)
[8] Irwin, J. O., The generalized Waring distribution, J. Roy. Stat. Soc. A, 138, 374-384 (1975), Part 3 · Zbl 0017.07707
[9] Johnson, N. L.; Kotz, S., Distributions in Statistics, (Continuous Univariate Distributions, Vol. 2 (1970), Houghton Mifflin Co: Houghton Mifflin Co Boston) · Zbl 0213.21101
[10] Kotz, S.; Shanbag, D. N., Some new approaches to probability distributions, Adv. Appl. Prob., 12, 903-921 (1980) · Zbl 0454.62085
[11] Morrison, D. G., On linearly increasing mean residual lifetimes, J. Appl. Prob., 15, 617-620 (1978) · Zbl 0383.60016
[12] Tague, J., The success-breeds-success phenomenon and bibliometric processes, J. Am. Soc. Inf. Sci., 32, 4, 280-286 (1981)
[13] Yule, G. U., The statistical Study of Literary Vocabulary (1944), Cambridge University Press
[14] Xekalaki, E., Chance mechanism for the univariate generalized Waring distribution and related characterizations, (Taillie, C.; Patil, G. P., Statistical Distributions in Scientific Work. Vol. 4. Models, Structures, and Characterizations (1981), D. Reidel Publ. Co: D. Reidel Publ. Co Dordrecht), 157-171 · Zbl 0482.62003
[15] Xekalaki, E., Hazard functions and life distributions in discrete time, Commun. Statist. - Theor. Meth., 12, 21, 2503-2509 (1983) · Zbl 0552.62008
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.