Minimax credibility

Let us consider the row of random variables The distribution belonging to the random variable Y j is assumed to be unknown. Equivalently we say that the distribution of Y j depends on an unknown parameter θ j and we use the abbreviation Each random variable Y j stands for the observed performance of the risk j j = 1, 2, ..., N. The problem is to estimate the pure premium μ(θ k ) from the observed performance Y k (Y k may be thought of as either a single observation or as a single statistic—e.g. the average—summarizing the experiences of the risk over a certain period of time).