Contributions to Statistical Techniques for Two And Three Dimensional Measurement Problems

Cover Contributions to Statistical Techniques for Two And Three Dimensional Measurement Problems
Contributions to Statistical Techniques for Two And Three Dimensional Measurement Problems
Lackritz, James Robert
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1-4 A/u * Since E(N )/A ->■ 1/y as A -> °°, A/u can be thought of as being approximately equal to E(N ), and an estimate for E(N*) can be obtained, similar to the one from Section 3.9. Defining M, - the number of phase ,1 features on the sample, I M. / ,1=1 J 1- I is a consistent estimator of E(M ).
However, the feature count in two dimensions is not as easily obtained as the intercept count in one dimension since very irregularly shaped phases make counting diffi- cult. Frequently, the planar
...sample section may have only one continuous feature for a certain phase, such as in viewing a large body of water in a land study situation.
63 Perhaps a more useful result could be obtained from a basic stereological result introduced in Chapter 2. Recall that E[boundary length for phase J features ]/A = -ttC. (0), where C, (h) is as defined in Section 2.3, for phase j. For this estimate to be used, an underlying process for cell modeling must be assumed, so that a form for C.(h) can be obtained.


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