Comparing relative importance of the same component in a series system in two environments

The relative performance of a component of a series system in two different environments is considered. The conditional probability of the failure of the system due to the failure of the specified component given that the system failed before time t is regarded as a measure of relative importance of the component to the system. A U-statistic test for checking the equality of the relative importance of the component to the system in two different environments against the alternative that the relative importance is smaller in one of the environments, is proposed. Some simulation results for estimating the power of the test are reported. The proposed test is applied to one real data set and it is seen that a different aspect of the data is brought out by this comparison than that by the comparisons of the absolute importance functions such as the subsurvival functions, considered in earlier studies.     

Models and methods for pairing data

This paper deals with models and methods for count data derived from observations on pairing phenomena. Pairs formed from “similar” members are excluded. Various models are considered and analyzed. Particular emphasis is on developing methods for testing whether particular pairs are prone to occur more or less often than expected by chance.     

On a multiple endpoints testing problem

In a clinical trial comparing drug with placebo, where there are multiple primary endpoints, we consider testing problems where an efficacious drug effect can be claimed only if statistical significance is demonstrated at the nominal level for all endpoints. Under the assumption that the data are multivariate normal, the multiple endpoint-testing problem is formulated. The usual testing procedure involves testing each endpoint separately at the same significance level using two-sample t-tests, and claiming drug efficacy only if each t-statistic is significant. In this paper we investigate properties of this procedure. We show that it is identical to both an intersection union test and the likelihood ratio test. A simple expression for the p-value is given. The level and power function are studied; it is shown that the test may be conservative and that it is biased. Computable bounds for the power function are established.     

Demographic change, macroeconomic conditions, and the murder rate: The case of the United States, 1934–2006

Fluctuations in aggregate crime rates contrary to recent shifts in the age distribution of the U.S. population have cast doubt on the predictive power of the age–crime hypothesis. By examining a longer time horizon, back to the early 1930s, we show that the percentage of the young population is a robust predictor of the observed large swings in the U.S. murder rate over time. However, changes in the misery index—the sum of the inflation and unemployment rates—significantly contribute to explaining changes in the murder rate. This applies, in particular, to those changes that are at odds with the long-run trend of the U.S. age distribution, such as the decline in the murder rate in the latter part of the 1970s or its increase starting around the middle of the 1980s.     

A study of BIB designs through support matrices

This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given.     

Some new factor screening designs using the search linear model

Factor screening designs for searching two and three effective factors using the search linear model are discussed. The construction of such factor screening designs involved finding a fraction with small number of treatments of a 2^m factorial experiment having the property P_2t (no 2t columns are linearly dependent) for t=2 and 3. A ‘Packing Problem’ is introduced in this connection. A complete solution of the problem in one case and partial solutions for the other cases are presented. Many practically useful new designs are listed.     

Goodness-of-fit tests for a heavy tailed distribution

We study the Kolmogorov–Smirnov test, Berk–Jones test, score test and their integrated versions in the context of testing the goodness-of-fit of a heavy tailed distribution function. A comparison of these tests is conducted via Bahadur efficiency and simulations.     

On the equivalence of two approaches to simplicity in the analysis of block designs and some related results

Two seemingly different approaches to simplicity in the analysis of connected block designs, and their relationship to the concepts of balance are discussed.     

Optimality and bias of some interpolation and extrapolation designs

We consider interpolation and extrapolation designs with controlled bias. A consistent estimate of an upper bound of the bias is presented. The estimate of some extrapolated value is obtained in a two-stage procedure. The first one provides an estimate of some interpolated value. The second one uses a Taylor expansion around this point. This procedure yields a new type of designs. We discuss their optimality properties with respect to the variance and the bias.     

Multivariate inverse Gaussian distribution as a limit of multivariate waiting time distributions

Multivariate inverse Gaussian distribution proposed by Minami [2003. A multivariate extension of inverse Gaussian distribution derived from inverse relationship. Commun. Statist. Theory Methods 32(12), 2285–2304] was derived through multivariate inverse relationship with multivariate Gaussian distributions and characterized as the distribution of the location at a certain stopping time of a multivariate Brownian motion. In this paper, we show that the multivariate inverse Gaussian distribution is also a limiting distribution of multivariate Lagrange distributions, which is a family of waiting time distributions, under certain conditions.