Statistical Methods and Basic Statistical Functions

The previous chapter has addressed the general problem of fitting a set of data with a smooth function or curve where the data set has either some random component or is generated from some transcendental function that can not be expressed in a closed mathematical form. The major objective of the chapter was to obtain a continuous functional representation of the data set which could be used either for publication of the data or for further analysis of the data set. This chapter and the next chapter continues some of the discussions of Chapter 7 with an emphasis on the analysis of the statistical properties of data sets and on the fitting of data sets to physical models for the purpose of estimating various parameters of the model — sometimes called “parameter estimation”. There are a broad range of such applications to data analysis and data fitting. In most data fitting applications, the interest in not only in obtaining a smooth curve which gives a good visual representation of the data, but also in determining how accurately various model parameters can be estimated from the experimental data. This is where the statistical properties of the data become important. This emphasis on confidence limits of the parameters associated with data fitting is what distinguishes the examples in this chapter and the next chapter from the previous chapter. The present chapter concentrates on developing various statistical methods that are useful in data analysis and the next chapter concentrates on parameter estimation for data in the presence of random noise using many of the statistical properties developed in this chapter