Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Forecasting is a common data science task that helps organizations with capacity planning, goal setting, and anomaly detection. Despite its importance, there are serious challenges associated with ...

Forecasting at scale

Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions

complexity These procedures can be used whenever the observed levels of significance are available for all individual tests It is shown that both the Holm and Shaffer procedures can be improved under the assumption of positive orthant dependence for the test statistics It is noted that this assumption is met in many important practical situations and recommended that in these cases the new procedure be used in place of its predecessors whenever the required observed significance levels are available The methodology is illustrated with a numerical example

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An Improved Sequentially Rejective Bonferroni Test Procedure

Analysis of Type-II progressively hybrid censored data

In life testing, type I and type II censoring may be combined to form a hybrid life test. Epstein (1954) introduced this testing scheme and Epstein (1960b) proposed a two-sided confidence interval to estimate the mean lifetime, 8, of an exponential lifetime following such a test. His conjecture is modified slightly and a proof is given that establishes the validity of the proposed confidence interval.

A Confidence Interval for an Exponential Parameter from a Hybrid Life Test

Many times, aspects of populations exist that must satisfy a stochastic ordering requirement. Nevertheless, estimates may not bear out this stochastic ordering because of the inherent variability of the observations. This article will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases (a) one survival function being fixed in advance and (b) estimating two survival functions when the data include censored observations. A numerical example is discussed in detail to illustrate the solution to this problem.

Maximum Likelihood Estimation of the Survival Functions of Stochastically Ordered Random Variables

Often, the probability of the simultaneous occurrence of dependent events can be well approximated by assuming them to be independent. Here, we discuss bounds on the error in using this procedure and conditions when under (or over) estimates occur. An inequality involving expectations of conditionally independent random variables is proven. Applications treat extreme values of exchangeable random variables and error probabilities for simultaneous inference. Bivariate dependence concepts treated by Lehmann are generalized to the multivariate case in such a way that relations valid for the bivariate case continue to hold.

Richard L. Dykstra

Papers

A Confidence Interval for an Exponential Parameter from a Hybrid Life Test

Maximum Likelihood Estimation of the Survival Functions of Stochastically Ordered Random Variables

Events which are Almost Independent

An isotonic regression algorithm

Independence and the Normal Distribution