A Robust Estimation Method for Parameters of Zero-Inflated Poisson Distribution

Abstract

The invention discloses a method for carrying out robust estimation on the parameters of a zero-expansion poisson distribution. The method which specifically comprises the following steps: 1, regrading the zero-expansion poisson distribution as a mixed distribution of a degenerate distribution {X = 0} and a nonzero poisson distribution; 2, extracting nonzero data from zero-expansion data, and sequencing the nonzero data in an increasing order; 3, carrying out robust estimation on the mean value of the zero-expansion poisson distribution by using the median, widened median, mean mid-value and trisecting value of the nonzero data; 4, obtaining the robust estimation of a parameter lambda by using the relation between the mean value of the zero-expansion poisson distribution and the parameter lambda of the zero-expansion poisson distribution; and 5, based on the robust estimation of the parameter lambda, obtaining the robust estimation of a parameter p of the zero-expansion poisson distribution by using maximum likelihood estimation. The method disclosed by the invention provides a parameter robust estimation method for the zero-expansion poisson distribution, and then the robust estimation on the parameters of the zero-expansion poisson distribution is obtained further, therefore, the problem that the zero-expansion poisson distribution is easily affected by exceptional values can be effectively solved, and the difficulty in recognition of outliers in the zero-expansion data can be avoided.

Description

technical field [0001] The invention provides a robust estimation method for zero-inflated Poisson model (ZIP) parameters, and is suitable for related fields such as manufacturing, quality control, disease monitoring, and social science. Background technique [0002] Count data with a large number of "zero" values ​​widely exists in many fields, such as industrial production, quality control, service industry, disease monitoring, species research, etc. In a stable production process, due to the good process capability, the number of observed defects is "zero" in most cases, and the observed data at this time are shown as zero-inflated data; Work injury data are also often zero-inflated data. Because of the improvement of production technology and guarantee conditions, workers will not be injured in most cases. In this way, the number of workers injured is often "zero"; in the medical field, asthma is a common clinical For the subject, it may be a healthy person or an asthma...

AI Technical Summary

Problems solved by technology

[0005] (1) Purpose of the present invention: Aiming at the problem that the zero-inflated Poisson distribution is easily affected by outliers, a method for robust estimation of distribution parameters is proposed

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