The Interval Estimation Of Multi-parameter Distribution Based On The Monte Carlo Method

Monte Carlo simulation is a kind of statistical sampling test methods based on "random numbers" generation of certain distribution, which is by John von Neumann in 1940 first proposed.This paper studies and implements multi-parameter interval estimation algorithm based on the Monte Carlo method. In the model of parameter, the exact estimation needs to calculate the inverse function of distribution, while the Monte Carlo method can avoid to calculate the inverse function of the distribution by approximately simulating the distribution of statistics; at the same time, the traditional interval estimation methods more depend on large sample conclusion of the central limit theorem, when the actual problem is not in the sample size, the method of this article demonstrates its advantages which can be more accurately approximate confidence intervals.Specific contents include:The first chapter describes the contents of this paper, the research background, research significance and present research situation;The second chapter describes the principles, ideas and implementation of single and multi-parameter interval estimation based on Monte Carlo simulation;The third chapter is part of the case study. Firstly, based on the example of the location parameter and the percentile of the normal distribution, we introduce the implementation in multi-parameter interval estimation by the Monte Carlo method in detail, and compare with two classical algorithms, which proves the validity and feasibility of the method. Furthermore, by the use of two-parameter interval estimation algorithm based on Monte Carlo method in this paper, we achieve the interval estimation of mean difference and standard deviation ratio in the double normal distribution.The last chapter is summary and outlook.In this article, we derive the theory and algorithms of three interval estimation, comparing numerical results of interval estimation between the traditional method and ours, discussing the pros and cons as well as the limitation of the algorithm. In particular, We calculate the interval estimation of mean difference and standard deviation ratio in the double normal distribution by the combination of Monte Carlo simulation method and the two-parameter model, and the results is better.