The main objective of this dissertation is to predict the IBNR reserve. For this, it was developed a statistical model of combined distributions looking for a new distribution that fits the data well. The IBNR reserve, short for Incurred But Not Reported, represents the amount that insurers need to have to pay for the claims that occurred in the past but have not been reported until the present date. Given the importance of this reserve, several methods for estimating this reserve have been proposed. One of the most used methods for the insurers is the Chain Ladder, which is based on run-off triangles; this is a format of grouping the data according to the occurrence and the reported date. However this format causes the lost of important information. This dissertation, based on other articles and works that consider the data not grouped, proposes a new model for the non-aggregated data. The proposed model combines the delay in the claim report distribution represented by a log normal truncated (because there is only information until the last observed date); the total amount of claims incurred in a given period modeled by a Poisson distribution and the number of claims occurred in a certain period and reported until the last observed date characterized by a binomial distribution. Finally, the IBNR reserve was estimated by this method and by the chain ladder and the prediction capacity of both methods will be evaluated. Although the delay distribution seems to fit the data well, the proposed model obtained inferior results to the Chain Ladder in terms of forecast.