Summarize our project work in progress. Seek the coorperation to write papers. Mailing me. Click the title to read more..

Why we do - CLT problems

Central limit theorem is the wide and usefull thoerem of the staitical analysis, but it has the problem in practices and applicaitions.

1. The Z score of sample mean is not tested.

   1.1. We don’t know how many samples can make the sampling distribuiton of the Z score of sample mean approximate to the Z distribution.

   1.2. We don’t know what factors affect the sampling distribuiton of the Z score of sample mean approximat to the Z distribution.

   1.3. We never display the process of the approximation of the sampling distributon to the Z distribution for non normal distribuiton.

2. Not all the distributions are testd, but the central limit theorem is applied on all distribuitons.

3. Otehrs.

What we do

1. Generate random samples from a sepecific probability distribuiton and follow the steps to obtain the distribuiton of the sum of the random samples.

2. Confirm the factors that affect the sampling distribuiton apporximated to Normal distribuiton or the Z distribution.

How we work

1. Based on the number generating, not on the numerical analysis (needing the function known first), find the numbers’ pattern to understand the central limit theorem and find the minimal sample size that can let the sum of the random samples or the sample mean approximate to Normal distribuiton or the Z distribuiton.

2. Use the method and technology of probability distribuiton simulator to generate numbers randomly and do the variable transformation to get the random samples summed or the sample mean. Of course, that can calculate the sample variance, standard deviation, and so on. Then rest coefficeints is not the content of this project, but is the future project that I want to do.

3. Use five methods/processes to investigate Central limit theorem for each probability distribuiton.

What we find

This is the short video to summary the work.