By Bickel and Doksum
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K. 2, for simplicity let us write Xi for a typical observation from the population Πi , i = 1, . . , k. Then, show that max P{Xi > c} = P{Xj > c} 1≤i≤k if and only if Xj corresponds to the population with location parameter µj = µ[k] , the largest location parameter, whatever be the real number c. 1 Continued): Suppose that X1 , . . d. random variables from a universe having the N (µ, σ 2 ) distribution with −∞ < µ < ∞, 0 < σ < ∞. We assume that µ is unknown but σ is known. Let us test a simple null hypothesis H0 : µ = µ0 versus a simple alternative hypothesis H1 : µ = µ1 (< µ0 ) at the preassigned level α, 0 < α < 1.
These are also readily available in Chapter 2 of Ghosh et al. (1997). The emphasis here is to apply these results. 1 (Stein, 1956):: Let U1 , U2 , . . d. real valued random variables such that P(U1 = 0) < 1. Let a and b be real numbers, a < b, and N be the smallest integer j(≥ 1) for which the inj equality a < l=1 Ul < b is violated. Then there exists constants c(> 0) and 0 < r < 1 such that P(N > n) ≤ crn for n ≥ 1. The following result goes by the name Fundamental Identity of Sequential Analysis or Wald’s Fundamental Identity.
3 for different values of σ and come to the same conclusion. 48σ. OUT or any other file with a name no more than nine characters long. This file can be printed on any printer using either PRINT or COPY DOS commands. OUT will be erased and the current output results will be written into the file. OUT file listing after the programs Power and ProbKn executed in that order. 1: Suppose that X1 , . . d. random variables from a universe having the N (µ, σ 2 ) distribution with −∞ < µ < ∞, 0 < σ < ∞.