The non-central negative binomial distribution: Further properties and applications

Abstract

The non-central negative binomial distribution is both a mixed and compound Poisson distribution with applications in photon and neural counting, statistical optics, astronomy and a stochastic reversible counter system. In this paper various important probabilistic properties of the non-central negative binomial distribution in practical applications like log-concavity, discrete self-decomposability, unimodality, asymptotic behavior and tail length of the probability distribution have been derived. The construction as a mixed Poisson process by specifying a joint distribution for the inter-arrival times and its application is illustrated by a fit to real life data set.     

You're all I need to get by? Analyzing young entrepreneurs’ networks in Morocco from a “quantified narratives” method

The embeddedness of entrepreneurs in a network of social relations has been largely documented by the literature since the seminal work of Granovetter. In different contexts, it has been shown that the entrepreneurial network plays a central role in the creation of their business and provides a variety of resources. Few studies, however, seek to understand the motivations of entrepreneurs when they mobilize a tie, and the effects of these mobilizations on the content and quality of this relationship. From a fieldwork undertaken in Morocco, we implement a “quantified narratives” method which codes each sequence of access to a resource in the course of the start-up in order to map the network of relationships of young innovative entrepreneurs. We go further than previous studies using this method in that we develop a multivariate model that enables us to build hypotheses from qualitative material analysis and to test them econometrically. This case study highlights more generally the interest of mixed methods in analyzing complex mechanisms like network mobilization and their motivations. We analyze the different logics which led entrepreneurs to the mobilization of the network at the time of the creation of their business. The main result that emerges is that the family is sidelined in obtaining funding. This original result is indicative of the tension faced by these young Moroccan entrepreneurs: the need to grow their business is sometimes in contradiction with the desire to create through it a space of autonomy gained on the family.     

A new mixed chain sampling plan based on the process capability index for product acceptance

This article proposes a new mixed chain sampling plan based on the process capability index C_pk, where the quality characteristic of interest follows the normal distribution with unknown mean and variance. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications. In order to construct the tables, the problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.     

Income Security During Sickness Absence. What Do British Middle‐classes Do?

Income maintenance during sickness absence is an under‐researched field within social policy analysis, and yet it is conducive to exploring the interplay between statutory, corporate and private forms of income protection. Drawing on original qualitative interview data, the article shows that British middle‐class couples largely ignore or dismiss public provision, which is due to a relatively low level of sickness benefits, but also based on misconceptions about social rights and the role of employers as mandatory (and voluntary) sick pay providers. Despite a considerable degree of mistrust, mortgage‐related private sickness insurance mattered to some extent, although this does not necessarily reflect policyholders’ strategic choices vis à vis current household needs for income security. Other potential sources of income replacement, such as savings, are relied on much less. In general, the analysis shows a heavy middle‐class reliance on, and strong confidence in, employer‐based sickness pay. This finding may be contrasted with questions about the sustainability of voluntary corporate provision, as well as its capacity to provide income security for the workforce as a whole.     

A mixed membership model-based measure for subgroup integration in social networks

Social networks analysis often involves quantifying subgroup structure in which tie density is greater among nodes in the same subgroup than between subgroups. One such measure, subgroup insularity or segregation, is the extent that subgroups are separate from each other. We introduce a new measure, γ, which is a parameter from the mixed membership stochastic blockmodel (MMSBM; Airoldi et al., 2008), and differs from many existing measures in that γ does not depend on node membership. We compare this measure to several well-known measures and use simulation studies and real data analysis to provide insight into how this measure can be used in practice.     

MULTI-STAGE KERNEL-BASED CONDITIONAL QUANTILE PREDICTION IN TIME SERIES

We present a multi-stage conditional quantile predictor for time series of Markovian structure. It is proved that at any quantile level, p ∈ (0, 1), the asymptotic mean squared error (MSE) of the new predictor is smaller than the single-stage conditional quantile predictor. A simulation study confirms this result in a small sample situation. Because the improvement by the proposed predictor increases for quantiles at the tails of the conditional distribution function, the multi-stage predictor can be used to compute better predictive intervals with smaller variability. Applying this predictor to the changes in the U.S. short-term interest rate, rather smooth out-of-sample predictive intervals are obtained.     

Pride and prejudice: opposing constructions of mixed race in Australia

ABSTRACT

In the Australian context, the development of a ‘situated politics of mixedness’ is complicated by the fact that there are (at least) two main categories of mixed race populations – the Indigenous and the migrant/settler. For those with mixed Aboriginal/non-Aboriginal ancestries, and those with mixed White and other migrant ancestries, life chances and identities differ significantly. This paper outlines some of these differences using the trope of pride and prejudice. For those of mixed migrant/settler heritage, evidence is growing that the mixed experience is predominantly one of pride. For them, misrecognition, or being asked about their racial background, is an opportunity for play, often resulting in ‘the big reveal’ of a valorised mixed identity associated with something other than a bland ‘white bread’ Australian-ness. For those of mixed Indigenous heritage however, there remains a significant level of prejudice, not (only) for being Aboriginal, but for not being visibly Aboriginal enough. Using existing studies and a number of media controversies as examples, this paper interrogates the implications of these differences for understandings of the ways in which race is recruited in the construction of legitimate identity claims. It asks particularly how ‘mixed race’ is helpful analytically to describe the identity constructions within these two very different experiences.     

Estimation of the Lognormal-Pareto Distribution Using Probability Weighted Moments and Maximum Likelihood

This article deals with the estimation of the lognormal-Pareto and the lognormal-generalized Pareto distributions, for which a general result concerning asymptotic optimality of maximum likelihood estimation cannot be proved. We develop a method based on probability weighted moments, showing that it can be applied straightforwardly to the first distribution only. In the lognormal-generalized Pareto case, we propose a mixed approach combining maximum likelihood and probability weighted moments. Extensive simulations analyze the relative efficiencies of the methods in various setups. Finally, the techniques are applied to two real datasets in the actuarial and operational risk management fields.     

A NOTE ON VARIANCE ESTIMATION FOR THE GENERALIZED REGRESSION PREDICTOR

The generalized regression (GREG) predictor is used for estimating a finite population total when the study variable is well‐related to the auxiliary variable. In 1997, Chaudhuri & Roy provided an optimal estimator for the variance of the GREG predictor within a class of non‐homogeneous quadratic estimators (H) under a certain superpopulation model M. They also found an inequality concerning the expected variances of the estimators of the variance of the GREG predictor belonging to the class H under the model M. This paper shows that the derivation of the optimal estimator and relevant inequality, presented by Chaudhuri & Roy, are incorrect.