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独立指数寿命串联系统的置信区间AI 解读

Suppose X1, X2, ···, Xn are independent identically distributed exponential random variables with parameter λ1. Let Y1, Y2, ···, Ym also be independent identically distributed exponential random variables with parameter λ2, and assume that X's and Y's are independent. The problem is to estimate R(t) = e−(λ1+λ2)t. A procedure for determining on exact (1 − α) level lower confidence bound for R(t) is presented. let U = min(Σn t = 1Xi, Σm i = 1Yi), and K = {largest i ≤ n: Σj i −…

独立指数寿命串联系统的置信区间AI 解读

Suppose X1, X2, ···, Xn are independent identically distributed exponential random variables with parameter λ1. Let Y1, Y2, ···, Ym also be independent identically distributed exponential random variables with parameter λ2, and assume that X's and Y's are independent. The problem is to estimate R(t) = e−(λ1+λ2)t. A procedure for determining on exact (1 − α) level lower confidence bound for R(t) is presented. let U = min(Σn t = 1Xi, Σm i = 1Yi), and K = {largest i ≤ n: Σj i −…

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回归中的同时容忍区间AI 解读

Joint prediction intervals (based upon the original fitted model) for K future responses at each of K separate settings of the independent variable have been treated by Lieberman (1961). When K is unknown and possibly arbitrarily large, these results do not apply. A solution to the problem of arbitrary K is given in terms of tolerance intervals on the distributions of future observations, the intervals being (probabilistically) simultaneous in each possible value of the…

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