Research on the Mathematical Model of Gauss's Error Distribution

• 1、Riztec Research Institute, Zhongshan City, Guangdong Province

Abstract：Normal distribution is a mathematical model derived and proved by Gauss when he studies the error distribution. The error distribution derived by Gauss specifically refers to the estimation error distribution. There are standard error distribution and zero error distribution in statistical practice. They form a complete error distribution system. Analyze Gauss\'s normal distribution and correct the inconsistency of the two parameters. Three mathematical models of error distribution are established. Error distribution belongs to the category of theoretical distribution and reflects the digital characteristics of the nature of statistical objects. Unimodal distribution belongs to the category of actual distribution, symmetrical normal distribution asymmetrical skew distribution, which reveals the distribution law of statistical objects. The difference between Gaussian normal distribution and Gaussian error distribution is that the former is the actual distribution and the latter is the theoretical distribution. Actual distribution and theoretical distribution together provide a new statistical tool and method for statistical analysis and prediction of large data.

Keywords： ErrEstimation error distribution Standard error distribution Zero error distribution Unimodal distribution Normal distribution Skewed distribution