infonet-economy

Extreme value data with a high clump-at-zero occur in many domains. Moreover, it might happen that the observed data are either truncated below a given threshold and/or might not be reliable enough below that threshold because of the recording devices. This situations occurs in particular with radio audience data measured using personal meters that record environmental noise every minute, that is then matched to one of the several radio programs. There are therefore genuine zeroes for respondents not listening to the radio, but also zeroes corresponding to real listeners for whom the match between the recorded noise and the radio program could not be achieved. Since radio audiences are important for radio broadcasters in order for example to determine advertisement price policies, possibly according to the type of audience at di_erent time points, it is essential to be able to explain not only the probability of listening a radio but also the average time spent listening the radio by means of the characteristics of the listeners. In this paper, we propose a generalized linear model for zero-infated truncated Pareto distribution (ZITPo) that we use to fit audience radio data. Because it is based on the generalized Pareto distribution, the ZITPo model has nice properties such as model invariance to the choice of the threshold and from which a natural residual measure can be derived to assess the model fit to the data. From a general formulation of the most popular models for zero-inated data, we derive our model by considering successively the truncated case, the generalized Pareto distribution and then the inclusion of covariates to explain the non-zero proportion of listeners and their mean listening time. By means of simulations, we study the performance of the maximum likelihood estimator (and derived inference) and use the model to fully analyze the audience data of a radio station in an area of Switzerland.