Data Modeling Using Quantile and Density-Quantile Functions

摘要

Statistical data modeling is a field of statistical reasoning that seeks to fit models to data without using models based on prior theory; rather one seeks to learn the model by a process which could be called statistical model identification. When analyzing a sample X sub 1, ..., X sub n, statisticians should not confine themselves to either fitting a Gaussian distribution, or transforming the data to be Gaussian. Such an approach ignores the importance of bimodality as a feature of observed data, and also ignores the need to fit to data probability model based distributions which could suggest probability models for the causes generating the data. This paper describes an approach to statistical data modeling which emphasizes estimation of quantile and density-quantile functions; it treats the Gaussian distribution as just one of the available distributions. (Author)