Book reviews

S.M.Kendall:Multivariate Analysis.Charles Griffin & Co. Ltd., London and High Wycombe 1975, 210 pp

C.T.Leondes (ed.):Control and Dynamic Systems, Advances in Theory and Applications. Vol. 11, Academic Press, New York and London 1974, 516 pp., $ 24.50.

CH. R.Nelson:Applied Time Series Analysis for Managerial Forecasting. Holden Day, Inc., San Francisco 1973, 231 pp., $ 14.95.

B.DE Finetti:Theory of Probability. Vol. 1, 2, John Wiley & Sons, New York, London, Sydney, Toronto. Vol. 1, 1974, 300 pp., £ 7.50 - Vol. 2 1975, 375 pp., £ 10.50.

P.Erdördos, J. Spencer:Probabilistic Methods in Combinatorics. Akadémic Press, New York and London; Akadémiai Kiadó, Budapest 1974, 106 pp., $ 11.75.

J.S.R.Ustagi:Variational Methods in Statistics.Academic Press, New York and London 1975.

J.S.Rustagi:Optimizing Methods in Statistics.Academic Press, New York and London 1971,488 pp., $ 17.00.

Karl V. Bury:Statistical Models in Applied Science. John Wiley & Sons, New York-London-Sydney-Toronto 1975,.625 pp., £ 15.60; $ 28.00.

Michael R. Anderberg:Cluster Analysis for Applications. Academic Press, New York-San Francisco-London 1973, 359 pp., $ 27,–.

J.L.Fleiss:Statistical Methods for Rates and Proportions. John Wiley & Sons, New York-London-Sydney-Toronto 1973. 223 pp., £ 6.50.

J.Tanur et al. (Ed.):Statistics:A Guide to the Unknown. Holden Day, Inc., San Francisco 1972, 430 pp.

H.VÁliaho, T. Pekkonen:A Procedure for Stepwise Regression Analysis.Akademie-Verlag, Berlin 1976, 90 pp., 18,– M.

M.Reinfeldt, U. TrÁnkle:Signifikanztabellen statistischer Testvertellungen. R. Oldenbourg Verlag, Mnchen, Wien 1976, 151 S., DM 44,–.

R.E.Barlow, D.J.Batholomew, J.M.Bremner, H.D.Brunk:Statistical Inference Under Order Restrictions.(The Theory and Applications of Isotonic Regression.) John Wiley & Sons, New York 1972, 388 pp., £ 7.50.

H.J.Larson:Introduction to Probability Theory and Statistical Inference. Wiley, New York 1974, 430 pp., £ 6.85.

R.A.Carlson:Statistics. Holden Day, Inc., San Francisco 1973, 393 pp.

E. Page:Queueing Theory in OR. Butterworths, London 1972, 187 pp., £ 3.60.

H.Krampe, J.Kubat, W.Runge:Bedienungsmodelle. Ein Leitfaden für die praktische Anwendung, Verlag Die Wirtachaft, Berlin 1973, 512 S., 79,– M.

G.S.Fishman:Concepts and Methods in Discrete Events Digital Simulation. John Wiley & Sons, New York 1973, 385 pp., £ 8,75.     

Maximum likelihood estimation of the bimodal failure rate for censored and tied observations

DIMITROV, RACHEV and YAKOVLEV ( 1985 ) have obtained the isotonic maximum likelihood estimator for the bimodal failure rate function. The authors considered only the complete failure time data. The generalization of this estimator for the case of censored and tied observations is now proposed.     

Parameter measures of skewness

Several different measures of skewness are commonly used in place of γ₁, the third central moment divided by the cube of the standard deviation. The numerical values of these measures are compared in this paper for members of the gamma, lognormal or Weibull family of distributions and shown to vary considerably in most cases even when skewness and kurtosis are moderate.     

Tests for Symmetry Based on the One-Sample Wilcoxon Signed Rank Statistic

ABSTRACT

The one-sample Wilcoxon signed rank test was originally designed to test for a specified median, under the assumption that the distribution is symmetric, but it can also serve as a test for symmetry if the median is known. In this article we derive the Wilcoxon statistic as the first component of Pearson's X ² statistic for independence in a particularly constructed contingency table. The second and third components are new test statistics for symmetry. In the second part of the article, the Wilcoxon test is extended so that symmetry around the median and symmetry in the tails can be examined seperately. A trimming proportion is used to split the observations in the tails from those around the median. We further extend the method so that no arbitrary choice for the trimming proportion has to be made. Finally, the new tests are compared to other tests for symmetry in a simulation study. It is concluded that our tests often have substantially greater powers than most other tests.