A new generalized Weibull distribution in income economic inequality curves

Researchers have been developing various extensions and modified forms of the Weibull distribution to enhance its capability for modeling and fitting different data sets. In this note, we investigate the potential usefulness of the new modification to the standard Weibull distribution called odd Weibull distribution in income economic inequality studies. Some mathematical and statistical properties of this model are proposed. We obtain explicit expressions for the first incomplete moment, quantile function, Lorenz and Zenga curves and related inequality indices. In addition to the well-known stochastic order based on Lorenz curve, the stochastic order based on Zenga curve is considered. Since the new generalized Weibull distribution seems to be suitable to model wealth, financial, actuarial and especially income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. Also, the estimation of parameters by maximum likelihood and moment methods is discussed. Finally, this distribution has been fitted to United States and Austrian income data sets and has been found to fit remarkably well in compare with the other widely used income models.     

A semiparametric approach for modelling multivariate nonlinear time series

In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada     

Paving the Way for A Normal Life: A Qualitative Study of Coping Strategies Among Iranian Divorced Women

Regarding the devastating aftermath of divorce among Iranian divorced women, which is mainly affected by sociocultural factors, this qualitative study was conducted to explore their applied strategies in reorganizing their lives. Data collection started through deep unstructured interviews followed by semistructured interviews with 18 divorced women who were chosen by purposive sampling from mental health clinics, social work centers, or available cases. Gathered data were analyzed using the qualitative content analysis method. Two main themes—behaviors of self-preservation and abstinence and struggling for balance—emerged. Subcategories were concealing the divorce, feminine self-restriction, avoidance behaviors, replacement of losses, seeking support, role development, handling the tensions, and defending oneself against the divorce failure. This study provides comprehensive knowledge of how Iranian divorced women reregulate their lives and also highlights their unique and culture-based coping strategies. Therefore, it provides specialists with a context-specific foundation for mental health care and enables them to intervene more effectively.     

Monitoring and change-point estimation for spline-modeled non-linear profiles in phase II

In some applications of statistical quality control, quality of a process or a product is best characterized by a functional relationship between a response variable and one or more explanatory variables. This relationship is referred to as a profile. In certain cases, the quality of a process or a product is better described by a non-linear profile which does not follow a specific parametric model. In these circumstances, nonparametric approaches with greater flexibility in modeling the complicated profiles are adopted. In this research, the spline smoothing method is used to model a complicated non-linear profile and the Hotelling T² control chart based on the spline coefficients is used to monitor the process. After receiving an out-of-control signal, a maximum likelihood estimator is employed for change point estimation. The simulation studies, which include both global and local shifts, provide appropriate evaluation of the performance of the proposed estimation and monitoring procedure. The results indicate that the proposed method detects large global shifts while it is very sensitive in detecting local shifts.     

Parametric Estimation of Menarcheal Age Distribution Based on Recall Data

Menarche, the onset of menstruation, is an important maturational event of female childhood. Most of the studies of age at menarche make use of dichotomous (status quo) data. More information can be harnessed from recall data, but such data are often censored in a informative way. We show that the usual maximum likelihood estimator based on interval censored data, which ignores the informative nature of censoring, can be biased and inconsistent. We propose a parametric estimator of the menarcheal age distribution on the basis of a realistic model of the recall phenomenon. We identify the additional information contained in the recall data and demonstrate theoretically as well as through simulations the advantage of the maximum likelihood estimator based on recall data over that based on status quo data.     

On the relation between Wiener index and eccentricity of a graph

Journal of Combinatorial Optimization - The relation between the Wiener index W(G) and the eccentricity $$\varepsilon (G)$$ of a graph G is studied. Lower and upper bounds on W(G) in terms of...     

On the exact joint distribution of a linear combination of order statistics and their concomitants in an exchangeable multivariate normal distribution

In this work we prove that for an exchangeable multivariate normal distribution the joint distribution of a linear combination of order statistics and a linear combination of their concomitants together with an auxiliary variable is skew normal. We also investigate some special cases, thus extending the results of Olkin and Viana (J Am Stat Assoc 90:1373–1379, 1995), Loperfido (Test 17:370–380, 2008a) and Sheikhi and Jamalizadeh (Paper 52:885–892, 2011).     

On a Selection Weibull Distribution

In this article, a selection Weibull distribution is investigated. First, some properties and representations of the model with some plots of the density and hazard rate functions are illustrated. Second, some simple relations of this model with some distributions discussed. In addition, maximum likelihood estimators obtained with numerical methods, and compared by three sub-models with a data set that shows the performance of our model. Finally, a simulation study presented for all parameters.     

Efficient reassembling of graphs,part 1: the linear case

The reassembling of a simple connected graph \(G = (V,E)\) is an abstraction of a problem arising in earlier studies of network analysis. Its simplest formulation is in two steps:

1. (1)
   We cut every edge of G into two halves, thus obtaining a collection of \(n = |\,V\,|\) one-vertex components, such that for every \(v\in V\) the one-vertex component \(\{ v \}\) has \({{degree}}_{}(v)\) half edges attached to it.
    
2. (2)
   We splice the two halves of every edge together, not of all the edges at once, but in some ordering \(\Theta \) of the edges that minimizes two measures that depend on the edge-boundary degrees of assembled components.
    

A component A is a subset of V and its edge-boundary degree is the number of edges in G with one endpoint in A and one endpoint in \(V-A\) (which is the same as the number of half edges attached to A after all edges with both endpoints in A have been spliced together). The maximum edge-boundary degree encountered during the reassembling process is what we call the \(\varvec{\alpha }\) -measure of the reassembling, and the sum of all edge-boundary degrees is its \(\varvec{\beta }\) -measure. The \(\alpha \)-optimization (resp. \(\beta \)-optimization) of the reassembling of G is to determine an order \(\Theta \) for splicing the edges that minimizes its \(\alpha \)-measure (resp. \(\beta \)-measure). There are different forms of reassembling, depending on restrictions and variations on the ordering \(\Theta \) of the edges. We consider only cases satisfying the condition that if an edge between disjoint components A and B is spliced, then all the edges between A and B are spliced at the same time. In this report, we examine the particular case of linear reassembling, which requires that the next edge to be spliced must be adjacent to an already spliced edge. We delay other forms of reassembling to follow-up reports. We prove that \(\alpha \)-optimization of linear reassembling and minimum-cutwidth linear arrangment (\(\mathrm{CutWidth}\)) are polynomially reducible to each other, and that \(\beta \)-optimization of linear reassembling and minimum-cost linear arrangement (\(\mathrm{MinArr}\)) are polynomially reducible to each other. The known NP-hardness of \(\mathrm{CutWidth}\) and \(\mathrm{MinArr}\) imply the NP-hardness of \(\alpha \)-optimization and \(\beta \)-optimization.