The problem of estimation of the moment of time of the event occurrence for quadratic loss function

Evaluation of the time moment of the appearance of some events on the available statistical information is of considerable interest. In medicine, agricultural physics, reliability theory, risk analysis problems of this type arise often. The various restrictions on the choice of the moment time can be taken by virtue of the specific characteristics of this problem. One of the possible approaches to solving these problems is the use of fines and loss functions. In this paper we considered the quadratic loss. Different levels of awareness are considered and the optimal estimates are found. For unknown distribution function we suggest a minimax approach and the optimal solution is found also. Defective probability distributions are considered in the paper. Defective probability distributions are used in applied problems in medicine, in reliability theory, in risk analysis. Refs 6.