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二项随机变量对数的偏差与高阶累积量AI 解读

The bias and first four cumulants of the distribution of the logarithm of a binomial variate are studied by means of asymptotic expansions and exact computation. A new estimator of the variance is derived and evaluated. The asymptotic skewness is found to differ from the result of Walter (1975). Applications to point estimation of the one-hit curve and the interval estimation and testing of the ratio of binomial parameters are considered. Because of the bias and nonnormality…

二项随机变量对数的偏差与高阶累积量AI 解读

The bias and first four cumulants of the distribution of the logarithm of a binomial variate are studied by means of asymptotic expansions and exact computation. A new estimator of the variance is derived and evaluated. The asymptotic skewness is found to differ from the result of Walter (1975). Applications to point estimation of the one-hit curve and the interval estimation and testing of the ratio of binomial parameters are considered. Because of the bias and nonnormality…

The bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation. The covariance of the empirical logit and its estimated variance is derived. Neither the +½ correction of Haldane (1955) and Anscombe (1956) nor the −½ suggested by Cox (1970) for weighted logit regression is universally effective in reducing bias. Other corrections are considered. The distribution of the empirical…

经验 logit 的偏差、方差估计、偏度和峰度对加权最小二乘分析的影响AI 解读

The bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation. The covariance of the empirical logit and its estimated variance is derived. Neither the +½ correction of Haldane (1955) and Anscombe (1956) nor the −½ suggested by Cox (1970) for weighted logit regression is universally effective in reducing bias. Other corrections are considered. The distribution of the empirical…

零截断二项分布若干估计量的小样本表现AI 解读

Estimation of the parameter of a binomial distribution with the zero class truncated is a classical problem in human genetics. Mathematically the problem is the estimation of p from n, independent observations with distribution, (r s)prqs-r/(1 - qs) where r = 1, 2, ··· s, q = 1 - p and s ≥ 2 is a known integer. This article gives exact results which show the simple estimator of Mantel [17] to be less biased, both asymptotically and in small samples, than either the ML…

零截断二项分布若干估计量的小样本表现AI 解读

Estimation of the parameter of a binomial distribution with the zero class truncated is a classical problem in human genetics. Mathematically the problem is the estimation of p from n, independent observations with distribution, (r s)prqs-r/(1 - qs) where r = 1, 2, ··· s, q = 1 - p and s ≥ 2 is a known integer. This article gives exact results which show the simple estimator of Mantel [17] to be less biased, both asymptotically and in small samples, than either the ML…

有删失与无删失小样本中若干两样本检验的表现AI 解读

The power curves of three two-sample tests are compared in small samples from the exponential and four forms of the Weibull distribution with and without censoring. The tests considered are: F ratio, modified F ratio (F′ test), and a generalized Wilcoxon test (W test). Monte Carlo methods are used to obtain power curves for each test with sample sizes 20 and 50. The F test is known to be most efficient when sampling is from exponential distributions. If sampling is from…

The power curves of three two-sample tests are compared in small samples from the exponential and four forms of the Weibull distribution with and without censoring. The tests considered are: F ratio, modified F ratio (F′ test), and a generalized Wilcoxon test (W test). Monte Carlo methods are used to obtain power curves for each test with sample sizes 20 and 50. The F test is known to be most efficient when sampling is from exponential distributions. If sampling is from…