Methodology

The sample mean and variance of N independent observations from a random variable x are,

Assumption: a normal distribution in x.

1. Statistical convergence of the mean value

Confidence interval for mean value

where t_n is Student-t statistic and n = N-1. 

Or,

where,

Statistical convergence error of mean value

2. Statistical convergence of the variance value

Confidence interval for variance value

where χ_n is chi-square statistic and n = N-1.

Or,

where

Statistical convergence error of variance is defined as