# 11_16_11 - 3 0.352941 0.176471 0.259182 0.093759 0.082711 5...

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STAT 409 Examples for 11/16/2011 Fall 2011 X 1 , X 2 , … , X n Empirical Distribution Function: S ( x ) = [ number of X i ’s that are x ] / n H 0 : X 1 , X 2 , … , X n are i.i.d. with c.d.f. F ( x ) Test Statistic D = ( ) ( ) F S sup x x x - . 1. Consider a data set: 2 6 9 3 10 22 25 6 7 1 18 3 13 15 5 2 3 Consider H 0 : X 1 , X 2 , … , X 17 are i.i.d. Exponential with mean θ = 10. S ( x ) = [ number of X i ’s that are x ] / n = [ number of X i ’s that are x ] / 17 S ( x- ) = [ number of X i ’s that are < x ] / n = [ number of X i ’s that are < x ] / 17 F ( x ) = 1 – e x / 10 , x 0 x S(x) S(x-) F(x) |S(x)-F(x)| |S(x-)-F(x)| 1 0.058824 0 0.095163 0.036339 0.095163 2 0.176471 0.058824 0.181269 0.004799 0.122446

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Unformatted text preview: 3 0.352941 0.176471 0.259182 0.093759 0.082711 5 0.411765 0.352941 0.393469 0.018295 0.040528 6 0.529412 0.411765 0.451188 0.078223 0.039424 7 0.588235 0.529412 0.503415 0.084821 0.025997 9 0.647059 0.588235 0.59343 0.053628 0.005195 10 0.705882 0.647059 0.632121 0.073762 0.014938 13 0.764706 0.705882 0.727468 0.037238 0.021586 15 0.823529 0.764706 0.77687 0.04666 0.012164 18 0.882353 0.823529 0.834701 0.047652 0.011172 22 0.941176 0.882353 0.889197 0.05198 0.006844 25 1 0.941176 0.917915 0.082085 0.023261 D = 0.122446 < 0.25 ⇒ p-value > 0.20. Do NOT Reject H at α = 0.20 ....
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## This note was uploaded on 12/15/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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11_16_11 - 3 0.352941 0.176471 0.259182 0.093759 0.082711 5...

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