Résumé 221 :

Within actuarial jargon, an exposure curve is a distribution of the ratio between the limited expected loss at various limits and the unlimited expected loss. We present destruction rate models either defined by their distribution function or equivalently by their exposure curve. A particular attention is given to one-inflated distributions and the so-called MBBEFD distribution. Parameter estimation for these two models is carried out by maximum likelihood estimation and moment matching estimation. Properties of these estimators are studied. Finally, numerical illustrations are given in the actuarial context.