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基于无记忆性的指数分布拟合优度检验AI 解读

Summary In this investigation a test of goodness of fit for exponentiality is proposed. This procedure applies equally whether the scale and/or the location parameters of the distribution are known or not. The limiting null and non-null distributions of the test statistic are normal under minimal conditions. Monte Carlo critical values for small sample sizes are given and the power of the test is calculated for various alternatives showing that it compares favourably…

将部分拟合优度统计量修改为渐近正态零分布AI 解读

SUMMARY The Cramér-von Mises class of test statistics for the one-sample goodness-of-fit problem is based on the weighted L2-distance of the distribution from its empirical counterpart. It is well known that the root π standardized norm has a degenerate limiting distribution under the null hypothesis, and the π standardized norm has a nondegenerate limiting distribution that is not normal and depends on identifying the principal components for every weight function. Usually…

使零假设极限分布渐近正态的拟合优度统计量修正AI 解读

SUMMARY The Cramér-von Mises class of test statistics for the one-sample goodness-of-fit problem is based on the weighted L2-distance of the distribution from its empirical counterpart. It is well known that the root π standardized norm has a degenerate limiting distribution under the null hypothesis, and the π standardized norm has a nondegenerate limiting distribution that is not normal and depends on identifying the principal components for every weight function. Usually…

平均剩余寿命的新检验AI 解读

The mean residual life at age t is the expected value of the remaining life beyond that age. A new U-statistic is derived for testing constant versus decreasing mean residual life. The new test is easier to compute and performs better for several alternatives than previous tests.

平均剩余寿命的一种新检验AI 解读

The mean residual life at age t is the expected value of the remaining life beyond that age. A new U-statistic is derived for testing constant versus decreasing mean residual life. The new test is easier to compute and performs better for several alternatives than previous tests.

向量值二元失效率的非参数估计AI 解读

Let $\mathbf{X} = (X_1, X_2)'$ be a bivariate random vector distributed according to an absolutely continuous distribution function $F(\mathbf{x})$ which has first partial derivatives. Let $\bar{F}(\mathbf{x}) = P(X_1 > x_1, X_2 > x_2).$ The vector-valued bivariate failure rate is defined as $\mathbf{r}(\mathbf{x}) = (r_1(\mathbf{x}), r_2(\mathbf{x}))',$ where $r_i(\mathbf{x}) = -\partial \ln \bar{F}(\mathbf{x})/\partial x_i (i = 1, 2)$. In this paper, we propose a smooth…