A simple method for determining the limiting distribution of sample central moments for two-point and Binomial distributions
نویسندگان
1 Department of Statistics, College of Science, Payame Noor University, Tehran, Iran
2 Department of Statistics, College of Science, Payame Noor University, Tehran, Iran
3 Department of Statistics, College of Science, Payame Noor University, Tehran, Iran
4 Department of Statistics, College of Science, Payame Noor University, Tehran, Iran
doi
10.22034/jsmta.2023.20158.1100چکیده
Moments play an essential role in the characterization of statistical distributions and criteria such as dispersion, skewness, and kurtosis. This article is a dissection of the central moments of two-point and binomial distributions. First, we consider the Bernoulli distribution of the population and generalize the results. With a simple method, we present the condition that when the sample size is large, the structure of the sample central moment consists of random variables independent of standard normal or chi-square or a combination of both. In the obtained results, the role of points that have a probability of 1/2 is very influential in the limit distribution.
