On aggregating Benefit of the Doubt composite indicators

In this short communication, I propose a procedure to aggregate individual composite indicators (CIs) into a group CI (e.g., aggregate CI for a group of countries) that is based on the work of Färe and Zelenyuk (2003) that was originally presented in the efficiency measurement literature. It is shown that the implementation of the aggregation procedure into the CI-context is rather straightforward. To illustrate the procedure in the CI-setting, an aggregate CI for human development for the global EU-region is computed using the EU Member States’ HDI sub-indicators.     

Geometric composite indicators with compromise Benefit-of-the-Doubt weights

This paper builds on Van Puyenbroeck and Rogge's (2017) ‘indirect’ multiplicative Benefit-of-the-Doubt (BoD) index number framework, in which the linear, data-driven BoD-model is used to estimate the importance of various sub-indicators within a geometric composite index (CI). We present an integrated framework that combines optimistic and pessimistic BoD-based weighting that enables to (1) establish the degree of unbalance in countries’ policy portfolio mix, (2) identify multiple underlying factors to explain inter-temporal evolution, and (3) explain for differences in country policy performances under the different weighting schemes following a multiplicative Bortkiewicz decomposition. In doing so, we use alternative optimistic and pessimistic BoD-models as existing models suffer from potential drawbacks in the identification of a country's comparative strengths and weaknesses. We illustrate our results with social inclusion data for the EU-countries for the period 2008-2013.     

Construction project monitoring by means of RAM-based composite indicators

This paper aims to assess the performance of a sample of completed building projects in Oregon by employing the range-adjusted measure, a slack-based data envelopment analysis (DEA) model. In the first stage of analysis, project efficiency ratings (ie composite indicators) are derived using selected single performance indicators in a no-output model; whereas in the second stage, censored Tobit regression is employed to model the efficiency ratings. The results indicate that only four out of the 50 sample projects are efficient within the DEA context. Moreover, there is not much evidence for systematic effects of project size on DEA efficiency rating.     

On a family of aggregate claims distributions

This paper gives a family of aggregate claims distributions using an integral equation representation. The Kernel of the integral equation is chosen so that the compound distributions such as Poisson and binomial are members of the same family. Furthermore, the aggregate claims distribution can be determined by the mean and variance of the number of claims.     

On higher indicators of regular association schemes

In the present paper, we will define the higher Frobenius–Schur indicators and the higher indicators of association schemes as a generalization of those of finite groups. The higher indicators of any association scheme are always positive rational numbers. Especially, for any positive integer $n$, the $n$th indicator of any regular association scheme is the number of relations such that its strong girth divides $n$. Thus, all higher indicators of any regular association scheme are natural numbers, and the sequence of the indicators is periodic. We will show that the converses of these facts are also true for finite exponent association schemes. Finally, we introduce a family of infinite exponent association schemes all higher indicators of which are natural numbers and the sequence of the indicators of which is periodic.     

Analysis of the third European survey on working conditions with composite indicators

A composite indicator Working conditions for comparing European countries is constructed from data of the Third European Survey on Working Conditions. The main findings are as follows: (a) European countries differ with respect to working conditions statistically more significantly than with respect to earnings; it implies a quite accurate discrimination threshold in ranking countries with respect to working conditions, (b) working conditions and earnings positively correlate over the whole of Europe but correlate little within single countries; it indicates at the prevailing role of national determinants over professional or social specificities as contributing to the average working conditions, and (c) earnings play no essential role in subjective estimations, including job satisfaction, which mainly depends on working conditions; consequently, more attention should be paid to improving the latter.     

On composite twisted unknots

Following Mathieu, Motegi and others, we consider the class of possible composite twisted unknots as well as pairs of composite knots related by twisting. At most one composite knot can arise from a particular -twisting of an unknot; moreover a twisting of the unknot cannot be composite if we have applied more than a single full twist. A pair of composite knots can be related through at most one full twist for a particular -twisting, or one summand was unaffected by the twist, or the knots were the right and left handed granny knots. Finally a conjectured characterization of all composite twisted unknots that do arise is given.

     

On some composite functional inequalities

The aim of the paper is to deal with the following composite functional inequalities

On composite formal power series

Let be a holomorphic map from to defined in a neighborhood of such that . If the Jacobian determinant of is not identically zero, P. M. Eakin et G. A. Harris proved the following result: any formal power series such that is analytic is itself analytic. If the Jacobian determinant of is identically zero, they proved that the previous conclusion is no more true.

The authors get similar results in the case of formal power series satifying growth conditions, of Gevrey type for instance. Moreover, the proofs here give, in the analytic case, a control of the radius of convergence of by the radius of convergence of .

RÉSUMÉ. Soit une application holomorphe de dans définie dans un voisinage de et vérifiant . Si le jacobien de n'est pas identiquement nul au voisinage de , P.M. Eakin et G.A. Harris ont établi le résultat suivant: toute série formelle telle que est analytique est elle-même analytique. Si le jacobien de est identiquement nul, ils montrent que la conclusion précédente est fausse.

Les auteurs obtiennent des résultats analogues pour les séries formelles à croissance contrôlée, du type Gevrey par exemple. De plus, les preuves données ici permettent, dans le cas analytique, un contrôle du rayon de convergence de par celui de .

     

On the trace of the antipode and higher indicators

We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are, respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dimH. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.     

On the Distributions of Two Classes of Multiple Dependent Aggregate Claims

In this paper we examine two classes of correlated aggregate claims distributions, with univariate claim counts and multivariate claim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24： 19-32（1994）] and Wang ＆ Sobrero＇s [ASTIN Bulletin, 24：161-166 （1994）] concerning recursions for compound distributions to a multivariate situation where each claim event generates a random vector. Then we give a multivariate continuous version of recursive algorithm for calculating a family of compound distribution. Especially, to some extent, we obtain a continuous version of the corresponding results in Sundt [ASTIN Bulletin, 29：29-45 （1999）] and Ambagaspitiya [Insurance： Mathematics and Economics, 24：301-308 （1999）]. Finally, we give an example and show how to use the algorithm for aggregate claim distribution of first class to compute recursively the compound distribution.     

两类索赔相关风险模型的罚金折现期望函数

考虑两类索赔相关风险模型.两类索赔计数过程分别为独立的广义Poisson过程和广义Erlang(2)过程.得到了该风险模型的罚金折现期望函数满足的积分微分方程及该函数的Laplace变换的表达式,且当索赔额均服从指数分布时,给出了罚金折现期望函数及破产概率的明确表达式.     

On solving composite power polynomial equations

It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton's identities. In this work, by further exploring Newton's identities, we discover a binomial decomposition rule for composite elementary symmetric polynomials. Utilizing this decomposition rule, we solve three types of systems of composite power polynomial equations by converting each type to single-variable polynomial equations that can be solved easily. For each type of system, we discuss potential applications and characterize the number of nontrivial solutions (up to permutations) and the complexity of our proposed algorithmic solution.

     

On a correlated aggregate claims model with Poisson and Erlang risk processes

In this paper we consider a risk model with two dependent classes of insurance business. In this model the two claim number processes are correlated. Claim occurrences of both classes relate to Poisson and Erlang processes. We derive explicit expressions for the ultimate survival probabilities under the assumed model when the claim sizes are exponentially distributed. We also examine the asymptotic property of the ruin probability for this special risk process with general claim size distributions.     

随机累积相依索赔的矩及分布逼近

在索赔序列具有一阶自回归相依结构的条件下,给出了随机累积索赔前三阶矩的解析表达式,并应用矩匹配的方法讨论了所得结果在总索赔分布逼近中的应用.数值实验表明了结论的正确性和有效性.     

On ruin probability and aggregate claim representations for Pareto claim size distributions

We generalize an integral representation for the ruin probability in a Crámer-Lundberg risk model with shifted (or also called US-)Pareto claim sizes, obtained by Ramsay (2003), to classical Pareto(a) claim size distributions with arbitrary real values a>1 and derive its asymptotic expansion. Furthermore an integral representation for the tail of compound sums of Pareto-distributed claims is obtained and numerical illustrations of its performance in comparison to other aggregate claim approximations are provided.     

Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index

Composite indicators (CIs) are often used for benchmarking countries' performance, but they frequently stir controversies about the unavoidable subjectivity in their construction. Data Envelopment Analysis helps to overcome some key limitations, as it does not need any prior information on either the normalization of sub-indicators or on an agreed unique set of weights. Still, subjective decisions remain, and such modelling uncertainty propagates onto countries' CI scores and rankings. Uncertainty and sensitivity analysis are therefore needed to assess the robustness of the final outcome and to analyse how much each source of uncertainty contributes to the output variance. The current paper reports on these issues, using the Technology Achievement Index as an illustration.     

On the idempotency of some composite functors

We present examples of localization functors whose composition with certain cellularization functors is not idempotent.