The central limit theorem says that if you take infinite number of samples ( > 30) from a population, compute their mean values, and collect them, you will reach normal distribution. Is this valid for other parameters?
What I mean in this question is if we take infinite number of samples, compute their variances or any other parameter, and collect them, do we construct a normal distribution ?
Answer:
I made some researches to check if we can expand Central Limit Theorem for all parameters, and we could not find an academic or experimental document. However, I wrote its code. By using random number generator, I generated samples of numbers between 1 and 6, which means I imitated rolling dice problem. I created 100 000 samples and each of them consists of 300 observations(numbers). I drew its distribution plot with the help of Seaborn. As a result, Sampling distributions of sample variance and sample standard deviation are also like normal distribution.