Chapter 6 2114

# Chapter 6 2114 - Chapter 6 Point Estimation 1 Estimators...

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Unformatted text preview: Chapter 6 Point Estimation 1 Estimators Estimator - a rule that tells us how to calculate an estimate based on information in the sample. It is generally expressed as a formula. A point estimator of a parameter θ is a single number that can be regarded as a sensible value for θ . A point estimator can be obtained by selecting a suitable statistic and computing its value from the given sample data . For example: In Chapter 7 we will discuss interval estimation that provides rules that tell us how to calculate two numbers based on the sample data, forming an interval with a lower and upper limit within which the parameter is expected to lie. This pair of numbers is called an interval estimator , or more commonly a confidence interval . 2 θ ˆ ∑ = = n x x i μ ˆ n x p = ˆ 3 Consider these 20 observations on dielectric breakdown voltage for pieces of epoxy resin: 24.46 25.61 26.25 26.42 26.66 27.15 27.31 27.54 27.74 27.94 27.98 28.04 28.28 28.49 28.50 28.87 29.11 29.13 29.50 30.88 The pattern in the normal probability plot is quite straight, so we assume that the distribution of breakdown voltage is normal with mean value μ . Because normal distributions are symmetric, μ is also the median lifetime of the distribution. The given observations are then assumed to be the result of a random sample X 1 , X 2 , ..... X 20 from this normal distribution. Consider the following estimators and resulting estimates for the mean : Estimator = Estimate = = 555.86/20 = 27.793 Estimator = Estimate = (27.94 + 27.98)/2 = 27.960 Estimator = [min(X i )+ max(X i )]/2 = the average of the two extreme lifetimes Estimate = (24.46 + 30.88)/2 = 27.670 Estimator = 10% trimmed mean (discard the smallest and largest 10% of the sample and then average), Estimate = 555.86 - 24.46 - 25.61 - 29.50 - 30.88 16 = 27.838 x n x i / ∑ x ~ ) 10 ( tr x Unbiased and Minimum Variance Estimators...
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Chapter 6 2114 - Chapter 6 Point Estimation 1 Estimators...

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