Relation for joint densities of progressively censored order statistics

A relation between four joint densities of progressively type-II censored order statistics is shown, which is well known in the particular case of ordinary order statistics. The result leads to identities for product moments and for moments of contrasts.     

Bias Correction in Generalized Nonlinear Models with Dispersion Covariates

We derive general formulae for the second-order biases of maximum likelihood estimates of the parameters in generalized nonlinear models with dispersion covariates. This result generalizes previous work by Botter and Cordeiro (1998 Botter , D. A. , Cordeiro , G. M. ( 1998 ). Improved estimates for generalized linear models with dispersion covariates . J. Statist. Comput. Simul. 62 : 91 – 104 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Cordeiro and McCullagh (1991 Cordeiro , G. M. , McCullagh , P. ( 1991 ). Bias correction in generalized linear models . J. Roy Statist. Soc. B 53 : 629 – 643 . [Google Scholar]). The practical use of such bias corrections is illustrated in a simulation study.     

Social welfare,inequality, and poverty when needs differ

The paper examines income distributions of a finite population consisting of households which may differ with respect to needs. Since observed incomes are not directly comparable, income distributions have to be adjusted. Incomes are transformed to equivalent incomes interpreted as living standards and measured for a reference type, and the latter are supplemented by weights depending on needs. A general class of social welfare orderings (being based on adjusted rank-ordered income distributions) is characterized by a set of properties. Severe limitations for the form of the adjustment process are implied. The consequences for the measurement of inequality and poverty are demonstrated, and corresponding orderings are derived.     

Inference in a two-parameter generalized order statistics model

As a submodel of generalized order statistics with two unknown model parameters, m-generalized order statistics may serve as a simple model for ordered quantities in a given application. It is shown that the joint distribution of m-generalized order statistics has a representation as a regular exponential family in the model parameters, as it is the case for the comprising model. Utilizing this finding, a minimal sufficient and complete statistic is obtained along with distributional properties. Joint maximum likelihood estimation of the parameters is considered, and strong consistency and asymptotic efficiency of the estimator are established. A test is provided to decide whether a restriction to the submodel is reasonable.     

Mixed Methods – Stand der Debatte und aktuelle Problemlagen

While mixed methods research is already much advanced and institutionalized in textbooks, handbooks and its own journal on an international level, the German-language debate on mixed methods lags behind. Thus, this introductory paper starts with outlining the history and key concepts of mixed methods designs as well as the current state of the international debate. Next, we explain the aims and concept of this special issue as well as the crucial arguments of the single papers in the overall context of the special issues. Namely, the debate in this special issue of the Kölner Zeitschrift für Soziologie und Sozialpsychologie circles around the following four topics: philosophical, methodological and methodical foundations of mixed methods research; mixed methods designs and mixed methods sampling; modes of combining data and issues of validity; and process-oriented analysis, longitudinal analysis and evaluation. Based on the observations that, firstly, both the international social science research community and social problems are globalizing and, secondly, that social research itself is changing, especially by the increasing relevance of social media and big data, the paper concludes with suggestions for future research.     

Household decisions and equivalence scales

Considering an economy with a private good and a household good with a variable degree of publicness, we examine the consequences of two extreme decision rules: (1) the cooperative model, where households maximize the welfare of their members, and (2) the noncooperative model, where each household’s member maximizes her own utility. While publicness of the household good is necessary and sufficient for economies of size to exist and to increase with family size under cooperation, it is shown that this no longer holds in the absence of cooperation. On the other hand, the cooperative rule leads to less generous scales than the noncooperative one.      

Global stability of stochastic systems with Poisson distributed random time-delay

This paper gives global stability criteria for a controlled stochastic system with randomly distributed time-delay. The delay function is governed by a homogeneous Poisson process and is independent of the stochastic perturbation on the system. A delay-dependent gain controller is constructed and used to develop a stabilization criterion for the system. Based on the Lyapunov-Krasovskii functional method and stochastic analysis theory, notions of stochastic stability are examined in terms of linear matrix inequality and global stability criteria derived.     

A meta-analysis approach for step-stress experiments

The step-stress model is a special case of accelerated life testing that allows for testing of units under different levels of stress with changes occurring at various intermediate stages of the experiment. Interest then lies on inference for the mean lifetime at each stress level. All step-stress models discussed so far in the literature are based on a single experiment. For the situation when data have been collected from different experiments wherein all the test units had been exposed to the same levels of stress but with possibly different points of change of stress, we introduce a model that combines the different experiments and facilitates a meta-analysis for the estimation of the mean lifetimes. We then discuss in detail the likelihood inference for the case of simple step-stress experiments under exponentially distributed lifetimes with Type-II censoring.     

Equivalence Scales Reconsidered

The paper proposes a new and normative approach for adjusting households’ incomes in order to account for the heterogeneity of needs across income recipients when measuring inequality and welfare. We derive the implications for the structure of the adjustment method of two conditions concerned with the way the ranking of situations is modified by a change in the reference household type and by more equally distributed living standards across households. Our results suggest that concern for greater equality in living standards conflicts with the basic welfarist principle of symmetrical treatment of individuals that is at the core of the standard equivalence scale approach.