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.
Abbasi, N., Keshavarz, â., Yarmohammadi, â., & Saadatmand, A. (2023). A simple method for determining the limiting distribution of sample central moments for two-point and Binomial distributions. Journal of Statistical Modelling: Theory and Applications, 4(1), 1-10. doi: 10.22034/jsmta.2023.20158.1100
MLA
Narges Abbasi; ‎Narges Keshavarz; ‎Masoud Yarmohammadi; Abdollah Saadatmand. "A simple method for determining the limiting distribution of sample central moments for two-point and Binomial distributions". Journal of Statistical Modelling: Theory and Applications, 4, 1, 2023, 1-10. doi: 10.22034/jsmta.2023.20158.1100
HARVARD
Abbasi, N., Keshavarz, â., Yarmohammadi, â., Saadatmand, A. (2023). 'A simple method for determining the limiting distribution of sample central moments for two-point and Binomial distributions', Journal of Statistical Modelling: Theory and Applications, 4(1), pp. 1-10. doi: 10.22034/jsmta.2023.20158.1100
VANCOUVER
Abbasi, N., Keshavarz, â., Yarmohammadi, â., Saadatmand, A. A simple method for determining the limiting distribution of sample central moments for two-point and Binomial distributions. Journal of Statistical Modelling: Theory and Applications, 2023; 4(1): 1-10. doi: 10.22034/jsmta.2023.20158.1100
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