Estimation of the moment of time of event occurrence

The estimation of the moment of time of some event occurrence based on statistical data analysis causes a great interest in solving various application tasks. In medicine, agrophysics, reliability theory, risk analysis the problems of this type can occur quite often. In this case, because of the specific features of the application tasks there might be different restrictions on the choice of the moment of time. One of the possible approaches in solving this kind of tasks is the use of penalties and loss functions. This paper considers the various levels of awareness of the possible appearance of this type of events in different moments of time, with the optimal estimates are found. The optimal decision for known distribution function of the moment of time of some event occurrence is found. The distribution function can be estimated on the basis of statistical data. In the paper for unknown distribution function the minimax approach is suggested, with the optimal solution being found. Defective probability distributions are considered. Defective probability distributions are used in applied problems in medicine, reliability theory and risk analysis. Bibliogr. 4.