CEE597 Handout 20 Estimation of Lambda

CEE597 Handout 20 Estimation of Lambda - CEE 597 Risk...

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C E E 5 9 7 – R i s k A n a l y s i s a n d M a n a g e m e n t March 5, 2007 Risk Analyses in Transportation Systems (using statistics) Barnett, Abraham and Schimmel Airline Safety: Empirical Findings Barnett and Higgins Airline Safety: The Last Decade Flying & Driving See also: AirDisaster.Com, AirSafe.Com Please read for Monday 3/12/07: National Research Council, "55: A Decade of Experience," Exec. Summary How should λ of Poisson Process be estimated? How accurate is an estimate? Method of moments estimator Over time period T observe K arrivals. E[K] = λ T. Hence if observe that K equals k in this experiment, set k = ˆ ! T, and obtain ˆ = k/T. Bias of the estimator ˆ = K/T E[ ˆ ] = E[ K/T ] = E[ K ] /T = λ T /T = λ => Estimator unbiased!!! Variance of the estimator ˆ = K/T Var[ ˆ ] = Var[ K/T ] = E[ K ] /T 2 = λ T /T 2 = λ /T => variance of estimator decreases as 1/T with the time we watched County’s Infant death rate soars …. reported the headline of the16 Jan. 1990 Ithaca Journal , that went on to report that “… health experts who are shocked by the numbers are trying to find an explanation. Fourteen of every 1,000 babies born in the county during 1987 died probably before they could walk on their own.”
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C E E 5 9 7 – R i s k A n a l y s i s a n d M a n a g e m e n t March 5, 2007
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CEE597 Handout 20 Estimation of Lambda - CEE 597 Risk...

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