ESTIMATION OF THE INTENSITY OF MOTION OF EXTENDED OBJECTS USING A GENERALIZED WEIBULL DISTRIBUTION
V. M. Artyushenko1, V. I. Volovach2
1Technological University, Korolev, Moscow Region, Russia
2Volga State University of Service, Tol'yatti, Russia
Keywords: плотность распределения вероятностей, протяжённый объект, огибающая отражённого сигнала, критерий минимума условного риска, оценка параметра распределения, probability density, extended object, reflected signal envelope, criterion of minimum conditional risk, distribution parameter estimate
Abstract
The estimation of the scale parameter of a generalized Weibull probability density function is considered an analyzed by the minimum conditional risk criterion. Optimal estimates are obtained for the envelope intensity of signals reflected from extended objects provided that the intervals in the motion of these objects are independent of random variables. The above estimates are compared with the best unbiased estimate for various loss functions. It is shown that the risk convergence of the best unbiased estimate with the risk of an optimal estimate for the loss function equal to the error modulus is faster than the quadratic loss function. It is noted that optimal estimates for the invariant and power-law loss functions coincide. The lower and upper ε-confidence boundaries are obtained, and conditions under which these estimates correspond to estimates of the Weibull distribution parameter are determined
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