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利用截断性质刻画若干分布AI 解读

This article draws attention to some elementary results—that belong to the folklore of actuarial science—on the characterization of a reliability function S(x) by the “life expectancy” ℓy at age y and other expectations and moments of the residual life of a y survivor, whether the residual life is measured in the usual scale of time or a new scale. These provide closed-form expressions for models based on life expectancy or other truncated or generalized moments hypotheses.…

通过截断性质刻画若干分布AI 解读

This article draws attention to some elementary results—that belong to the folklore of actuarial science—on the characterization of a reliability function S(x) by the “life expectancy” ℓy at age y and other expectations and moments of the residual life of a y survivor, whether the residual life is measured in the usual scale of time or a new scale. These provide closed-form expressions for models based on life expectancy or other truncated or generalized moments hypotheses.…

随机球体的交集与球对称模型的非中心径向误差分布AI 解读

The paper gives an expression suitable for numerical computation and recursive relationships for the expected volume of the intersection of an $n$ dimensional sure sphere and an $n$ dimensional random sphere with a different radius, whose center follows a spherical distribution, the center of which does not coincide with that of the sure sphere. Several expressions are given for the distribution of the squared noncentral radial error when the vector observation follows a…