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Unformatted text preview: Goodness of fit test CASE 1: Parameters are KNOWN Random variable Y Sample data ,, Y1 Yn- Fi rst case: discrete case Y takes values from ,, y1 yk We are going to test whether the probability associated with each y is t rue Null Hypothesis: : = = , = H0 PY yi pi i 1 k : = = H1 PY y1 pi i 1 k We want to fit Y1 Yn into the diagram = = = # = m1 i 1n1Yi y1 of sample data to y1 = = = mk i 1n1Yi yk Y1 y2 .. yk Test statistics: = =- = ~- T0 i 1kmi npi2npi where Emi npi when n is large T0 xk 12 , If the test statistic T0 is large then the numerator is large in relationship . to denominator bad estimation , - Since this is a x2estimation we can calculate p values Method 1: - =- p value Pxk 12 T0 the larger the p value the better the estimation - Reject H0at any significance level p value Method 2: Confidence intervals .( , - Reject H0if T0is large reject H0if T0 x k 12 - % : ( , , - 1 100 CI 0 x k 12- Second case: Continuous Case Y takes value in interval , 0 yk Null hypothesis : - , = =...
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This note was uploaded on 07/22/2009 for the course IEOR 165 taught by Professor Shanthikumar during the Summer '08 term at University of California, Berkeley.
- Summer '08