Monotonicity of the Power Function and Unbiasedness of Some Likelihood Ratio Tests.
This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves. The main purpose of semi-linear credibility theory is the estimation of (the net premium for a contract with risk parameter ) by a linear combination of given functions of the observable variables: . So the estimators mainly considered here are linear...
En este artículo se realiza una discusión detallada de las principales metodologías empleadas para el estudio de fenómenos marginales y ocultos, como son el muestreo en bola de nieve, el método de estimación de captura-recaptura y el método para estimar el número de consumidores de cocaína en una gran ciudad. Este nuevo método se basa en dos selecciones aleatorias y puede estimar la ocultación del fenómeno.
We derive the exact distributions of R = X + Y, P = X Y and W = X / (X + Y) and the corresponding moment properties when X and Y follow Muliere and Scarsini's bivariate Pareto distribution. The expressions turn out to involve special functions. We also provide extensive tabulations of the percentage points associated with the distributions. These tables -obtained using intensive computer power- will be of use to the practitioners of the bivariate Pareto distribution.
In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided.