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By Larry Davis

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Right-hand sldeot h(r,1) : : : _ t • • • • • • • • • • • •• • • • • • • • • • • • • •• • • • • • • • • • • :· :',: :. " ·· .. " : : .. 5 : ~ : .. " .... ~ :. : :. : '" '". .. : : :. : .. 3 . PDF and CDF for the Normal Distribution. : :. : . 5 4 28 Chapter 3 • One-Dimensional Error Analysis variable r in h(r, a) should not be treated as a relative quantity. 3 is valid only for a == 1. In other words, the variable used for the horizontal axis has two interpretations, one for the CDF and another for the PDF.

L-_ _ -3 -2 -1 o 2 u 3 4 Comparison of the Standard Normal PDP with the PDP g(u) for n == 100. 6, respectively. m. m. m. m. m. m, respectively. 3) in AppendixA. One-Dimensional Error Analysis We start error analysis with the simplest kind-one-dimensional error analysis. Taking measurements of the height of a person, for example, or any measurement with a single degree of freedom, gives rise to this type of problem. We will be concerned mainly with normally distributed random variables. The normal (Gaussian) distribution is useful because it describes the random observations of most experiments, and it describes well the distribution of the estimation of parameters from most probability models (via the central limit theorem; see Appendix A).

Note that the curve corresponding to u = 0 is identical to the one-dimensional normal CDF and the curve corresponding to u = 1 is identical to the Rayleigh CDF. -----.... 68 : . 66 ~ "'C :::J . 98 . ------.... 65 . 7 . 5 u= cry/crx Probability Versus Ellipticity for p == 0 and R == 1 DRMS and R == 2DRMS. 2 ................ ; .. . : .. . ......... , : ~ :: ........ ; : 3~ ~ 2 . " .. : : . .. " " : .. . 4 ·1· '1' .. .. 9 ~ .. 6 .... ·1· . 8 Normalized Radius Versus Ellipticity for p == 0 and Various p Values.

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