Abstract
Abstract : This paper provides an overview to a new general approach to statistical data analysis and parameter estimation which could be called the quantile function approach. The aims of descriptive statistics (to graphically summarize and display the data) are obtained by Quantile-Box plots of the sample quantile function. The aims of goodness of fit are obtained by fitting smooth quantile functions to the sample quantile function. The aims of parameter estimation, especially robust estimation of location and scale parameters, are attained by regression analysis of the sample quantile function. (The goal of a statistician in analyzing a batch of data X1,...,Xn should be both estimation of parameters and goodness of fit. By 'goodness of fit' is meant fitting of the observed sample probabilities by a smooth probability law.)
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