Samuel Kotz

Breakthroughs in statistics

1.Introduction by R.E.Fancher. Galton, F.(1889) Co-relations and their measurement, chiefly from anthropometric data 2.Introduction by K.Dietz. McKendrick, A.G.(1926) Applications of mathematics to medical problems 3.Introduction by D.R.Cox. Yates,F.and Cochran,W.G.(1938) The analysis of groups of experiments 4.Introduction by P.K.Sen. Rao,C.R.(1948) Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation 5.Introduction by M.H.Gail. Cornfield,J.(1951) A method of estimating comparative rates from clinical data. Applications to cancer of the lung, breast and cervix 6.Introduction by M.Calder and R.A. Davis. Whittle,P.(1953) The analysis of multiple stationary time series 7.Introduction by E.Ronchetti. Daniels,H.E.(1954) Saddlepoint approximations in statistics 8.Introduction by I.J.Good. Cooley, J.W.and Turkey,J.W.(1965) An algorithm for the machine calculation of complex Fourier series 9.Introduction by R.J.Beran. H jek J.(1970) A characterization of limiting distributions of regular estimates 10.Introduction by T.L. Lai. Hastings, W.K.(1970) Monte Carlo sampling methods using Markov chains and their applications 11. Introduction

Dependent Relevations: Time-to-Failure Under Dependence

SYNOPTIC ABSTRACTKrakowski (1973) introduced the concept of the relevation, which is the conditional distribution of a random variable X2, given that it exceeds an independent random variable X1. This is relevant to failure time distributions when replacement is made from an aging stock.We develop analysis appropriate to relevation for dependent variables, and suggest it might be relevant if there is batch-to-batch variation, producing association between lifetimes of initial and replacement components.

A characterization of exponential distributions by a waiting time property

A characterization of exponential distributions based on the property that the waiting time variable Z = Tn-Y has the same distribution as each one of the independent random variables , provided Y has a uniform prior is presented.