1. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. FIGURES FOR CHAPTER 8 ESTIMATION OF PARAMETERS AND FITTING OF PROBABILITY DISTRIBUTIONS This chapter in the book includes: 8.1Introduction 8.2Fitting the Poisson Distribution to Emissions of Alpha Particles 8.3Parameter Estimation 8.4The Method of Moments 8.5The Method of Maximum Likelihood 8.6The Bayesian Approach to Parameter Estimation 8.7Efficiency and the Cramér-Rao Lower Bound 8.8Sufficiency 8.9Concluding Remarks 8.10Problems Return to ContentsReturn to Contents. ISBN 0-534-39942-8

2. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.1 Gaussian fit of current flow across a cell membrane to a frequency polygon.

3. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.2 Fit of gamma densities to amounts of rainfall for (a) seeded and (b) unseeded storms.

4. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.3 Gamma densities fit by the methods of moments and by the method of maximum likelihood to amounts of precipitation; the solid line shows the method of moments estimate and the dotted line the maximum likelihood estimate.

5. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.4 Histogram of 1000 simulated method of moment estimates of (a) α and (b) λ.

6. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.5 Plot of the log likelihood function of λ for asbestos data.

7. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.6 Histograms of 1000 simulated maximum likelihood estimates of (a) α and (b) λ.

8. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.7 Histogram of 1000 simulated maximum likelihood estimates of θ described in Example A.

9. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.8 20 confidence intervals for µ (left panel) and for σ2 (right panel) as described in Example A. Horizontal lines indicate the true values.

10. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.9 First statisticians prior (solid) and posterior (dashed). Second statisticians posterior (dotted).

11. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.10 Posterior distribution of.

12. © 2007 Thomson Brooks/Cole, a part of The Thomson Corporation. Figure 8.11 Asymptotic efficiencies of estimates of negative binomial parameters.