Abstract

The estimation of the scale parameter of the generalized Weibull probability density function by the criterion of the conditional risk minimum is considered and analyzed. Optimal estimates of the envelope intensity of the signals reflected from extended objects are obtained, provided that the intervals in the motion of these objects are independent random variables. These estimates are compared with the best unbiased estimate for various loss functions. It is shown that the convergence of the risk of the best unbiased estimate to the risk of the optimal estimate for the loss function, equal to the error module, is faster than the quadratic loss function. It is noted that the optimal estimates for the invariant and power loss functions coincide. The lower and upper \(\varepsilon\)-confidence boundaries are obtained and the conditions under which the obtained estimates correspond to the estimation of the Weibull distribution parameter are determined.

中文翻译：

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使用广义威布尔分布估计扩展对象的运动强度

摘要

考虑并分析了基于条件风险最小值准则的广义威布尔概率密度函数的尺度参数的估计。只要扩展对象反射的信号的包络强度是独立的随机变量，就可以获得最佳估计值。将这些估计值与各种损失函数的最佳无偏估计值进行比较。结果表明，损失函数等于误差模块的最优无偏估计风险与最优估计风险的收敛速度快于二次损失函数。注意，不变和功率损耗函数的最佳估计是一致的。上下\（\ varepsilon \）获得置信边界，并确定获得的估计对应于威布尔分布参数的估计的条件。