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Usually cross-sectional data are used instead of longitudinal data in the study of mortality because the cohort data has not a conclude distribution. Sometimes this choice can be questionable and not correct for the goal of the research. We introduce a new methodology that is useful to estimate the missing deaths and to construct the mortality table for an incomplete cohort. The Estimation-Maximization (EM) algorithm is generally employed when there are missing data and we want to compute the maximum likelihood. As model we used a mixture of distributions: one Half-Normal ad two Shew Normals. We tested the accuracy of the method comparing the estimate number of deaths obtained from the complete data with the estimates found by using EM algorithm. We employed the bootstrap method to compute the confidence intervals. We discovered that the two sets of measures are very close and the confidence intervals are not far from the true distribution. We applied our method to reconstruct the cohort data for different countries of the Human Mortality Database. We estimated the life expectancy at birth and also its confidence interval using bootstrapping.

birth cohort, EM algorithm, life expectancy, mixture model, skew normal