ENMA 420-520 Lecture 6 Slides_1

ENMA 420-520 Lecture 6 Slides_1 - Statistical Concepts for...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #6 Estimation Using Confidence Intervals 11
Background image of page 1

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

View Full DocumentRight Arrow Icon
10/17/09 Point Estimators A point estimator is a rule or formula that specifies how to calculate a numerical estimate based on measurements contained in a sample. The single number that results from the calculation is called a point estimate. Note the “^” accent used for estimates; e.g. an estimate of is 22
Background image of page 2
10/17/09 Biased vs. Unbiased A point estimator is calculated from a sample and therefore possesses a sampling distribution. The bias b(θ) of a point estimator is: A point estimator is said to be unbiased if the expected value of the parameter estimate is equal to the 33
Background image of page 3

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

View Full DocumentRight Arrow Icon
10/17/09 Minimum Variance Unbiased Estimator A small variance of the sampling distribution means most of the parameter estimates will tend to be close to the parameter Therefore, two desired characteristics for designing estimates are Minimum Variance Unbiased 44
Background image of page 4
10/17/09 Finding Point Estimators Method of Moments Method of Maximum Likelihood Method of Least Squares Other Methods 55
Background image of page 5

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

View Full DocumentRight Arrow Icon
10/17/09 Method of Moments Kth population moment: E(Yk) Kth sample moment: So … for 1st sample moment: Population moment is the population mean Sample moment is the sample mean 66
Background image of page 6
10/17/09 Maximum Likelihood The likelihood function L of a sample of n observations y1, y2, …, yn is the joint probability function p(y1, y2, …, yn) when Y1, Y2, … , Yn are discrete random variables. The likelihood function L of a sample of n observations y1, y2, …, yn is the joint probability function f(y1, y2, …, 77
Background image of page 7

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

View Full DocumentRight Arrow Icon
10/17/09 Maximum Likelihood (Cont’d) For random samples of n observations on a random variable Y, the likelihood function is: L = p(y1)p(y2)…p(yn) for discrete and L = f(y1)f(y2)…f(yn) for continuous Let L be the likelihood of a sample 88
Background image of page 8
10/17/09
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 54

ENMA 420-520 Lecture 6 Slides_1 - Statistical Concepts for...

This preview shows document pages 1 - 10. Sign up to view the full document.

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