Optimal Estimates of the Intensity of the Random Process with Generalized Weibull Distribution

The optimal estimates of the random flow intensity parameters of a point random process are determined under the condition that the intervals between events are related by a generalized Weibull distribution. The obtained estimates are compared with the unbiased estimates for different loss functions. Point and confidence estimates for the generalized Weibull distribution are described. The optimal unbiased estimator and its risk for a quadratic loss function are obtained. It is shown that the convergence of the risk of the unbiased estimator to the risk of the optimal correct estimator changes very slowly with increasing value of the existence condition of the optimal estimator. For the loss function equal to the error modulus, an optimal estimate is obtained. There is a rapid convergence of the risk of the unbiased score to the risk of the optimal correct score for the named function. It is shown that optimal estimates are the same for invariant and power loss functions. Upper and lower confidence bounds that are optimal for very general loss functions are obtained. The conditions are determined under which the found estimates meet the requirements for estimating the parameters of the Weibull distribution and also become the optimal estimates of the Poisson flow intensity.