Standardized Moment
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High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the kth standardized moment of a probability distribution is frac{mu_k}{sigma^k}! where k is the kth moment about the mean and is the standard deviation. It is the normalization of the kth moment with respect to standard deviation. The power of k is because moments scale as xk, meaning that k = k k: they are homogeneous polynomials of degree k, thus the standardized moment is scale invariant. This can also be understood as being because moments have dimension, but in the ratio defining standardized moments, the dimensions cancel, so they are dimensionless numbers.…mehr

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High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the kth standardized moment of a probability distribution is frac{mu_k}{sigma^k}! where k is the kth moment about the mean and is the standard deviation. It is the normalization of the kth moment with respect to standard deviation. The power of k is because moments scale as xk, meaning that k = k k: they are homogeneous polynomials of degree k, thus the standardized moment is scale invariant. This can also be understood as being because moments have dimension, but in the ratio defining standardized moments, the dimensions cancel, so they are dimensionless numbers.