LANL2008 - Approximate Confidence Intervals (CIs) for p...

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Unformatted text preview: Approximate Confidence Intervals (CIs) for p when Double Sampling (DS) Kenneth J. Ryan kjryan@bgsu.edu 1 Outline Notation and definitions. An example double sampling (DS) plan. Criteria for evaluating a CI procedure: Blyth and Still (1983) and Brown et al. (2001). The conservative DS CI procedures of Jennison and Turnbull (1983) and Duffy and Santner (1987). A new approximate DS Wilson CI procedure. Performance examples. 2 Notation and Definitions Let { X i } be a sequence of IID Bernoulli( p ) random variables. For n { 1 , 2 ,... } , define X n := ( X 1 ,X 2 ,...,X n ) S n := n X i =1 X i . Single sampling (SS) produces data X n for predetermined n . A complete and sufficient statistic for p is S n binom( n , p ). Double sampling (DS) produces data X n 2 if a S n 1 b and X n 1 otherwise for predetermined integers 0 a b n 1 < n 2 . A complete and sufficient statistic for p is ( N , S N ). 3 A DS Plan n 1 = 5, a = 1, b = 2, and n 2 = 8 6 S n- n h h h h h x h h h h h h h x h h h h h h x h h x h x x h h x h x x 5 8 1 2 (8,3) Stopping points : the black dots at which sampling terminates. 4 A DS Plan (cont.) n 1 = 5, a = 1, b = 2, and n 2 = 8 6 S n- n h h h h h x h h h h h h h x h h h h h h x h h x h x x h h x h x x 5 8 1 2 1 1 1 1 1 2 3 4 5 5 1 3 6 10 15 20 10 25 45 = C (8 , 3) C (8 , 3) = 45 is the path count from (0,0) to (8,3)....
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LANL2008 - Approximate Confidence Intervals (CIs) for p...

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