IEOR 165 Lecture 11 June 17 2009 COPY 1

IEOR 165 Lecture 11 June 17 2009 COPY 1 - Goodness of fit...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 : - , = =...
View Full Document

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.

Page1 / 5

IEOR 165 Lecture 11 June 17 2009 COPY 1 - Goodness of fit...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online