This paper investigates and evaluates an extension of the Akaike information criterion, KIC, which is an approximately unbiased estimator for a risk function based on the Kullback symmetric divergence. KIC is based on the observed-data empirical log-likelihood which may be problematic to compute in the presence of incompletedata. We derive and investigate a variant of KIC criterion for model selection in settings where the observed-data is incomplete. We examine the performance of our criterion relative to other well known criteria in a large simulation study based on bivariate normal model and bivariate regression modeling.

The main objective of this paper is to present a technique for pricing weather derivatives with payout depending on temperature. We start by using the Principle Component Analysis method to fill missing temperature data. Consequently, the cold and the warm periods were determined on the basis of a “clean” data by using a statistical approach. After that, we use historical data over a sufficient period to apply a stochastic process that describes the evolution of the temperature. A numerical example of a swap contract pricing is presented, using an approximation formula as well as Monte Carlo simulations.

Let $Y_1,Y_2\dots$ be independent observations of the income variable of some given population, with underlying distribution $G$. Given a poverty line $Z$, then for each $n\geq 1$, $q=q_n$ is the number of poor in the population. The general form of poverty measures used by economists to monitor the welfare evolution of this population is $$P_n=\frac{1}{a(q)b(n)}\sum^q_{j=1}c(n,q,j)d\left(\frac{Z-Y_{j,n}}{Z}\right).$$ This class includes the most popular poverty measures like the Sen, Shorrocks and Greer-Foster-Thorbecke statistics. We give a complete asymptotic normality theory in the framework of extreme value theory. In this paper, the poverty intensity is studied in two simple cases: Pareto and exponential distributions. Simulations and applications to the Senegalese data are given.

In the paper we have undertaken, with aid of the weighted Poisson distribution, to fit the count data collected in Republic of Congo-Brazzaville and related to a sample of spiraling whitefly Aleurodicus dispersus Russel (Homoptera: aleyrodidae) described by the preimaginal span (from eggs to adult stage) measured on days, the total number of eggs and the laying span. The linear regression issue between these three variables will be discussed as well.