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正态随机效应模型中覆盖准确的下容忍限AI 解读

A method for constructing accurate lower tolerance limits for the balanced one-way normal random-effects model is derived by conditioning on an estimator of the unknown expected mean square ratio. Simulation studies indicate that the present procedure is less conservative than that of several existing methods and gives more accurate coverage rates and smaller standard deviations. Numerical examples are given to illustrate the use of the new procedure. Tables needed to…

广义不完全修正贝塞尔分布的性质及可靠性应用AI 解读

In B. Harris [8], a family of distributions useful in statistical inference on the reliability of systems of independent parallel components was introduced. In the present article properties of this family of distributions are explored. The moments are obtained and asymptotic expressions for the mean and variance are given. Asymptotic normality is exhibited and relations to a number of special functions are indicated. Various asymptotic results and limit theorems are…

广义不完全修正贝塞尔分布的性质及其可靠性理论应用AI 解读

In B. Harris [8], a family of distributions useful in statistical inference on the reliability of systems of independent parallel components was introduced. In the present article properties of this family of distributions are explored. The moments are obtained and asymptotic expressions for the mean and variance are given. Asymptotic normality is exhibited and relations to a number of special functions are indicated. Various asymptotic results and limit theorems are…

泊松参数乘积与商的假设检验、置信区间及可靠性应用AI 解读

X1 X2, ···, Xk1, Y1, Y2, ···, Yk2 are k1 + k2 mutually independent Poisson random variables with parameters λ1, λ2, ···, λk1, μ1, μ2, ···, μk2, respectively. Confidence intervals and tests of hypotheses for the parameter θ = λ1λ2 ··· λk1 / μ1μ2 ··· μk2 are obtained. Under suitable conditions these procedures may be used to obtain approximate confidence intervals and tests of hypotheses of the parameter ρ = ρ1ρ2 ··· ρk1/ρk1+1ρk1+2 ··· ρk1+k2, where the ρi's, i = 1, 2, ···, k1…

经典占位问题的统计推断：类别数的无偏估计AI 解读

A random sample of N observations is obtained from a multinomial distribution with an unknown number θ of equiprobable cells. The existence and asymptotic properties of the unbiased estimator based on the number of occupied cells is given. The related problem in which observations are made sequentially, stopping after L repeated cells have been observed, is also discussed. In the fixed sample size case, if θ is known not to exceed N, the unbiased estimator is a ratio of…

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