Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings

It is known that the normal approximation is applicable for sums of non negative random variables, W, with the commonly employed couplings. In this work, we use the Stein’s method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of W. Applications of the main result to give the bound on normal approximation for binomial random variable, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are also provided.     

Similar coefficient for cluster of probability density functions

In this article, we propose a new criterion to evaluate the similarity of probability density functions (pdfs). We call this the criterion on similar coefficient of cluster (SCC) and use it as a tool to deal with overlap coefficients of pdfs in normal standard on [0;1]. With the support of the self-update algorithm for determining the suitable number of clusters, SCC then becomes a criterion to establish the corresponding cluster for pdfs. Moreover, some results on determination of SCC in case of two and more than two pdfs as well as relations of different SCCs and other measures are presented. The numerical examples in both synthetic data and real data are given not only to illustrate the suitability of proposed theories and algorithms but also to demonstrate the applicability and innovation of the proposed algorithm.     

Promoting sustainable development through civil society: A case study of the EU’s NSA/LA thematic programme in Kyrgyzstan

The article focuses on the contribution of the European Union (EU) in promoting sustainable development through the involvement of civil society in partner countries. More specifically, it analyses the main features and outcomes of the projects implemented by civil society organizations (CSOs) in Kyrgyzstan under the EU thematic programme Non‐State Actors and Local Authorities in Development (NSA/LA). Despite its importance—this is the only EU programme providing direct support to non‐state actors and local authorities engaged in poverty reduction—to date, there has been very little research on the functioning of this instrument on the ground. This article seeks to fill this gap in the literature by examining the EU’s contribution to sustainable development through a case study on Kyrgyzstan. The study is based on primary data: 10 semi‐structured interviews conducted with the EU‐funded organizations implementing the NSA/LA programme. The NSA/LA projects were analysed by considering two major fields of engagement of non‐state actors in the development process: as service providers and as advocates (Banks & Hulme, 2012). Overall, the organizations awarded EU support were not only focused on fulfilling short‐term needs but also sought to introduce new ways of dealing with poverty and inequality, positioning themselves between the “Big‐D” and the “little‐d” approaches to development (Bebbington, Hickey, & Mitlin, 2008). Nonetheless, the EU‐funded projects were too limited and fragmented to be able to sustain long‐term structural change. Therefore, the EU should place new emphasis on creating synergies between new and old structures at the grassroots level and establishing mechanisms and bodies that could merge and co‐ordinate their efforts. In addition, the calls for proposals could highlight the need to share the lessons learnt by “obliging” the beneficiaries to act as multipliers and to pass on their positive experience to neighbouring communities. Finally, the EU could stimulate the funded organizations to experiment with innovative mechanisms of involvement in the policy‐making process, by making this aspect a mandatory requirement of the projects implemented with its support.     

Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero‐inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log‐likelihood and the conditional Akaike information based on the joint log‐likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data‐generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log‐likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.     

Sum,product and ratio of Pareto and gamma variables

The exact distributions of X+Y, X Y and X/(X+Y) are studied when X and Y are independent Pareto and gamma random variables. Applications are discussed, to real problems in clinical trials, computer networks and economics.     

Simulating random variables using moment-generating functions and the saddlepoint approximation

When we are given only a transform such as the moment-generating function of a distribution, it is rare that we can efficiently simulate random variables. Possible approaches such as the inverse transform using numerical inversion of the transform are computationally very expensive. However, the saddlepoint approximation is known to be exact for the Normal, Gamma, and inverse Gaussian distribution and remarkably accurate for a large number of others. We explore the efficient use of the saddlepoint approximation for simulating distributions and provide three examples of the accuracy of these simulations.     

Non parametric mixture of strictly monotone regression models

In this article, we propose the non parametric mixture of strictly monotone regression models. For implementation, a two-step procedure is derived. We further establish the asymptotic normality of the resultant estimator and demonstrate its good performance through numerical examples.     

Optimal designs for additive mixture model with heteroscedastic errors

This paper presents a study of D- and A-optimality of direct sum designs for additive mixture models when the errors are heteroscedastic. Sufficient conditions are given so that D- and A-optimal designs for additive mixture models can be constructed from the D- and A-optimal designs for homogeneous models in sub-mixture systems.     

“零度写作”在中国的接受过程

“零度写作”在20世纪80年代末成为文学理论研究与文学作品评论类文章中频繁亮相的术语，研究界用“零度写作”评价新写实主义、先锋派等后现代写作。一方面借用“零度写作”对主体的解构，以“零度情感”评价新写实小说，另一方面将“零度写作”理解为摆脱意识形态、摆脱历史记忆的纯粹文学样式，从而将不再承载某种主流意识形态，标榜无意义或消解中心的后现代写作称为“零度写作”。但不同的学者站在捍卫或批判后现代写作的立场，令“零度写作”在中国遭遇了冰火两重天的局面。     

微言天算,零记号以及瞿昙历对中国古代数学的推进

本文论述我国古代天文历法的修定以及零记号的使用对数学计算的推进。