A Noncentral Lindley Construction Illustrated in an INAR(1) Environment

This paper proposes a previously unconsidered generalization of the Lindley distribution by allowing for a measure of noncentrality. Essential structural characteristics are investigated and derived in explicit and tractable forms, and the estimability of the model is illustrated via the fit of this developed model to real data. Subsequently, this model is used as a candidate for the parameter of a Poisson model, which allows for departure from the usual equidispersion restriction that the Poisson offers when modelling count data. This Poisson-noncentral Lindley is also systematically investigated and characteristics are derived. The value of this count model is illustrated and implemented as the count error distribution in an integer autoregressive environment, and juxtaposed against other popular models. The effect of the systematically-induced noncentrality parameter is illustrated and paves the way for future flexible modelling not only as a standalone contender in continuous Lindley-type scenarios but also in discrete and discrete time series scenarios when the often-encountered equidispersed assumption is not adhered to in practical data environments.

Structural modeling of the impact of bank nonperforming loans on the banking sector: the Ukrainian experience

The paper aims to develop scientific and methodological approach to assessing the interaction of nonperforming loans of Ukrainian banking institutions, the profitability of the banking sector and its financial stability, which will allow a more detailed assessment of the directions and degree of mutual influence of these elements. To substantiate this interaction economically and mathematically, structural equation modeling was chosen. Particularly, Statistica was chosen as a software tool to assess the adequacy of the resulting model and determine the level of statistical significance of its parameters. Six key indicators were selected as a research information base, two for each subject of research: indicators of nonperforming loans in the banking sector (the volume of nonperforming loans and the ratio of problem loans excluding capital reserves), profitability indicators of the Ukrainian banking sector (assets profit and rate of return on capital), and indicators of financial stability of the Ukrainian banking sector (regulatory capital-to-risk-weighted assets ratio and liquid assets-to-total assets ratio). For calculations, statistic data of selected indicators for 2005–2019 were used. As a result of calculations, mathematical data were obtained that accurately described the interaction of nonperforming loans of Ukrainian banking institutions, the profitability of the banking sector and its financial stability. The adequacy of the model was verified based on the following criteria: main summary statistics (ICSF criterion, ICS criterion, discrepancy function, maximum residual cosine), noncentrality fit indices (noncentrality parameter, population noncentrality parameter, Steiger-Lind RMSEA index, McDonald noncentrality index, adjusted population Gamma index), other single sample indices (Akaike information criterion, Schwarz criterion), and a normal probability plot.

A Unified Discussion on the Concept of Score Functions Used in the Context of Nonparametric Linkage Analysis

In this article we try to discuss nonparametric linkage (NPL) score functions within a broad and quite general framework. The main focus of the paper is the structure, derivation principles and interpretations of the score function entity itself. We define and discuss several families of one-locus score function definitions, i.e. the implicit, explicit and optimal ones. Some generalizations and comments to the two-locus, unconditional and conditional, cases are included as well. Although this article mainly aims at serving as an overview, where the concept of score functions are put into a covering context, we generalize the noncentrality parameter (NCP) optimal score functions in Ängquist et al. (2007) to facilitate—through weighting—for incorporation of several plausible distinct genetic models. Since the genetic model itself most oftenly is to some extent unknown this facilitates weaker prior assumptions with respect to plausible true disease models without loosing the property of NCP-optimality. Moreover, we discuss general assumptions and properties of score functions in the above sense. For instance, the concept of identical by descent (IBD) sharing structures and score function equivalence are discussed in some detail.

A Note on the Noncentrality Parameter and Effect Size Estimates for the F Test in ANOVA

The noncentrality parameter for the noncentral F is a precision-weighted sum of squares of treatment means, which is closely related to the test statistic and effect size. The two common effect size estimates are not based on the uniformly minimum variance unbiased (UMVU) estimate of the noncentrality parameter. The UMVU estimate of the noncentrality parameter implies a new and more conservative effect size estimate.