Computing Fresnel integrals via modified trapezium rules

In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially convergent as a function of N , the number of quadrature points, obtaining explicit error bounds which show that accuracies of 10−15 uniformly on the real line are achieved with N=12 , this confirmed by computations. The approximations we obtain are attractive, additionally, in that they maintain small relative errors for small and large argument, are analytic on the real axis (echoing the analyticity of the Fresnel integrals), and are straightforward to implement

On the EM algorithm for overdispersed count data

In this paper, we consider the use of the EM algorithm for the fitting of distributions by maximum likelihood to overdispersed count data. In the course of this, we also provide a review of various approaches that have been proposed for the analysis of such data. As the Poisson and binomial regression models, which are often adopted in the first instance for these analyses, are particular examples of a generalized linear model (GLM), the focus of the account is on the modifications and extensions to GLMs for the handling of overdispersed count data

How do consumers switch between close substitutes when price variation is small? The case of cigarette types

Tobacco, Logit model, Panel data, Heterogeneity, Bootstrapping, Household behavior, C33, C35, D12, I18,