Partial Ordering and Aging Properties of Order Statistics When the Sample Size is Random: A Brief Review

In many practical situations, order statistics arise naturally with random sample size. In this article, we review results on partial orderings and aging properties of such order statistics. The comparison of order statistics for different sample sizes is also discussed here.     

Evolution of recurrent asthma event rate over time in frailty models

Summary. To model the time evolution of the event rate in recurrent event data a crucial role is played by the timescale that is used. Depending on the timescale selected the interpretation of the time evolution will be entirely different, both in parametric and semiparametric frailty models. The gap timescale is more appropriate when studying the recurrent event rate as a function of time since the last event, whereas the calendar timescale keeps track of actual time. We show both timescales in action on data from an asthma prevention trial in young children. The frailty model is further extended to include both timescales simultaneously as this might be most relevant in practice.     

On a differential equation approach to the weighted orthogonal Procrustes problem

The weighted orthogonal Procrustes problem, an important class of data matching problems in multivariate data analysis, is reconsidered in this paper. It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated. This formulation has two important implications: that the weighted orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. The proposed approach is illustrated by numerical examples.     

Education,Work and Parenthood: Comparing the Experience of Young Men and Women in Sweden

This article analyzes the determinants of young men and women’s entry into parenthood, applying hazard regressions to a combination of longitudinal micro-data from the 1992/1993 Swedish Family Survey and aggregate time-series data. We study the impact of education, labor market attachment and macro-economic change on becoming a parent for both men and women in Sweden since the mid-1960s. Our results show clear gender differences both when it comes to individual characteristics and aggregate-level factors. Even though the effects sometimes differed according to gender, education and labor market attachment were key factors determining the transition to parenthood. Over time the pattern grew increasingly similar for men and women.     

Properties of the elasticity of a continuous random variable. A special look at its behavior and speed of change

Belzunce et al. (1995 Belzunce, F., Candel, J., Ruiz, J.M. (1995). Ordering of truncated distributions through concentration curves. Sankhya 57:375–383. [Google Scholar]) define the elasticity for non negative random variables as the reversed proportional failure rate (RPFR). Veres-Ferrer and Pavía (2012 Veres-Ferrer, E.J., Pavía, J.M. (2012). La elasticidad: una nueva herramienta para caracterizar distribuciones de probabilidad. Rect@ 13:145–158. [Google Scholar], 2014b Veres-Ferrer, E.J., Pavía, J.M. (2014b). On the relationship between the reversed hazard rate and elasticity. Stat. Pap. 55:275–284.[Crossref], [Web of Science ®] , [Google Scholar]) interpret it in economic terms, extending its definition to variables that can also take negative values, and briefly present the role of elasticity in characterizing probability distributions. This paper highlights a set of properties demonstrated by elasticity, which shows many similar properties to the reverse hazard function. This paper pays particular attention to studying the increase/decrease and the speed of change of the elasticity function. These are important properties because of the characterizing role of elasticity, which makes it possible to introduce our hypotheses and knowledge about the random process in a more meaningful and intuitive way. As a general rule, it is observed the need for distinguishing between positive and negative areas of the support.     

Modelling consumers' use of products

Patterns of consumers' use of products are of interest to manufacturers. This paper is concerned with modelling diary data on the use of one product, shampoo, recorded to the nearest hour by over 500 men during 1 week. A binary response multilevel model is developed, building on similar models for consumer purchase data. The model allows for a dependence on the number of days since last use. The results of fitting various versions of this model are discussed. A problem is that the number of days since last use is missing for all times up to the first use. An approximate EM approach is considered to deal with this problem.     

A compound Rayleigh survival model and its application to randomly censored data

Received: May 5, 1999; revised version: June 15, 2000     

连续铸造灰铁管内沟形成机理的探讨

本文通过测量内结晶器的变形,研究了内沟与石墨化膨胀及内结晶器变形的关系,指出了产生内沟的原因及其位置,为减少内沟提供了一定根据。