Some multivariate singular unified skew-normal distributions and their application

Abstract

We introduce here the truncated version of the unified skew-normal (SUN) distributions. By considering a special truncations for both univariate and multivariate cases, we derive the joint distribution of consecutive order statistics X_{(r, ..., r + k)} = (X_(r), ..., X_{(r + K)})^T from an exchangeable n-dimensional normal random vector X. Further we show that the conditional distributions of X_{(r + j, ..., r + k)} given X_{(r, ..., r + j ? 1)}, X_{(r, ..., r + k)} given (X_(r) > t)?and X_{(r, ..., r + k)} given (X_{(r + k)} < t) are special types of singular SUN distributions. We use these results to determine some measures in the reliability theory such as the mean past life (MPL) function and mean residual life (MRL) function.     

An examination of social work interventions for use with displaced Iraqi households in Jordan

The purpose of this paper is to identify and examine how models of social work intervention are being used with displaced Iraqi households in Jordan. The review of the situation of displaced Iraqis in Jordan identifies the size, characteristics and experiences of this group, Jordanian government policies towards them, and the role of IGOs and NGOs dealing with them. The literature review of social work interventions with refugees internationally identifies a range of psycho-social and community-based intervention models that are contextual, some of which include spiritual dimensions. The paper reviews social work interventions in use with Iraqi households in Jordan and concludes that these need to be focused at the individual, household and community levels using an inter-professional, holistic approach that includes spiritual dimensions, and that coordination between agencies is essential.     

Theorizing the social: Émile Durkheim's theory of force and energy

This paper offers a new interpretation of Émile Durkheim's The Elementary Forms of Religious Life (1912) as the basis for reconsidering the Tarde–Durkheim debate of 1903 and the distinctions between a theory of social force and a theory of social assemblage. Resisting traditional interpretations of Durkheim's scientism, this essay traces how concepts of force and energy are centrally developed in Elementary Forms to draw new lines between epistemology to ontology for twentieth-century theory. I argue that Durkheim develops an ‘energetic epistemology’ that conceives of the human capacity for shared meaning as a product of invested energy in the form of continually enacted and evolving material practice, thought, and attention. According to Durkheim, when a member of a collective perceives a god or feels belief, he or she actually perceives the accumulated energy of on-going creation and maintenance of objects and ideas by members of a collective. Sacred objects, images, and ideas bear the trace of collective energy the more they are carefully crafted, maintained in spaces that are specially arranged, and written into behavioural codes. This reading of Durkheim allows us to consider him in a lineage of social constructivists and, particularly, in relation to Ludwik Fleck, who has been largely confined to different theoretical discussions when his contributions to sociology have been acknowledged at all. By reconsidering Durkheim, we have occasion to rethink his sociology and understand how he redrew the lines between thought and action, between epistemology and ontology, through the material framework of energy and force.     

Multivariate normal mean-variance mixture distribution based on Lindley distribution

This article introduces a new asymmetric distribution constructed by assuming the multivariate normal mean-variance mixture model. Called normal mean-variance mixture of the Lindley distribution, we derive some mathematical properties of the new distribution. Also, a feasible maximum likelihood estimation procedure using the EM algorithm and the asymptotic standard errors of parameter estimates are developed. The performance of the proposed distribution is illustrated by means of real datasets and simulation analysis.     

Translating evidence into practice in childbirth: A case from the Occupied Palestinian Territory

ObjectiveTo investigate possible changes in practices during normal childbirth by implementing interventions which reduce the frequency of: intravenous fluids; bladder catheterization; analgesia; artificial rupture of membranes; oxytocin use for augmentation; vaginal examination; episiotomy, and increase: mobility; oral intake of fluids; and initiation of immediate breastfeeding.DesignAn operational research design.SettingA referral governmental hospital in the Occupied Palestinian Territory (oPt) between 2006 and 2010.Participants2345 women (baseline: 134 women, intervention: 1860 women, post-intervention: 351 women) and 17 providers (10 midwives and 7 physicians).InterventionsMultifaceted interventions; a combination of on-the-job training, audit, and feedback, supported by a core team and informal meetings.Main outcome measuresChange of practices during normal childbirth according to best evidence and the WHO recommendations.FindingsSignificant sustained improvements in practices during childbirth from baseline to post-intervention including artificial rupture of membranes, liberal use of oxytocin to augment normal labour, intravenous fluids, frequency of vaginal examinations, oral intake, immediate breastfeeding and routine episiotomy (P < 0.005). There was positive change in the mobility during labour, but this change was not sustained after 9 months from intervention to post-intervention. The usage of analgesia did not change.Key conclusionsCertain changes in practices during normal childbirth were possible in this hospital. A combination of on-the-job training with other interactive approaches increased midwives’ awareness, capacities and self-confidence to implement fewer interventions during normal labour.     

On distribution function estimation with partially rank-ordered set samples: estimating mercury level in fish using length frequency data

We study the non-parametric estimation of a continuous distribution function F based on the partially rank-ordered set (PROS) sampling design. A PROS sampling design first selects a random sample from the underlying population and uses judgement ranking to rank them into partially ordered sets, without measuring the variable of interest. The final measurements are then obtained from one of the partially ordered sets. Considering an imperfect PROS sampling procedure, we first develop the empirical distribution function (EDF) estimator of F and study its theoretical properties. Then, we consider the problem of estimating F, where the underlying distribution is assumed to be symmetric. We also find a unique admissible estimator of F within the class of nondecreasing step functions with jumps at observed values and show the inadmissibility of the EDF. In addition, we introduce a smooth estimator of F and discuss its theoretical properties. Finally, we expand on various numerical illustrations of our results via several simulation studies and a real data application and show the advantages of PROS estimates over their counterparts under the simple random and ranked set sampling designs.     

Order statistics and their concomitants from multivariate normal mean–variance mixture distributions with application to Swiss Markets Data

In this article, by considering a multivariate normal mean–variance mixture distribution, we derive the exact joint distribution of linear combinations of order statistics and their concomitants. From this general result, we then deduce the exact marginal and conditional distributions of order statistics and their concomitants arising from this distribution. We finally illustrate the usefulness of these results by using a Swiss markets dataset.     

A skew factor analysis model based on the normal mean–variance mixture of Birnbaum–Saunders distribution

This paper presents a robust extension of factor analysis model by assuming the multivariate normal mean–variance mixture of Birnbaum–Saunders distribution for the unobservable factors and errors. A computationally analytical EM-based algorithm is developed to find maximum likelihood estimates of the parameters. The asymptotic standard errors of parameter estimates are derived under an information-based paradigm. Numerical merits of the proposed methodology are illustrated using both simulated and real datasets.     

Robust binary regression

Robust procedures increase the reliability of the results of a data analysis. We studied such a robust procedure for binary regression models based on the criterion of least absolute deviation. The resulting estimating equation consists in a simple modification of the familiar maximum likelihood equation. This estimator is easy to compute with existing computational procedures and gives a high degree of protection.