Statistical Distributions
Creo Parametric Tolerance Analysis Extension powered by CETOL Technology represents all distributions in terms of scaled moments. The moments used are mean, standard deviation, skewness, and kurtosis. Scaled moments are calculated from the central moments (moments about the mean) of the statistical distribution.
Mean
The distribution mean represents the average (or expected) value of the population.
μ = distribution mean
Standard Deviation
Standard deviation (σ) is a measure of the spread of a distribution. It is the square root of the second central moment (variance):
where:
μ2 = second central moment, variance
Skewness
Skewness is a measure of the symmetry of a distribution. A skewness of 0 indicates a perfectly symmetric distribution. It is related to the third central moment. Since all distributions in Creo Tolerance Analysis are assumed to be symmetric, the value for skewness is always zero.
where:
μ3 = third central moment
Kurtosis
Kurtosis is a measure of the peakedness of a distribution or, conversely, the weight of the distribution tails. It is related to the fourth central moment. Kurtosis is labeled B2 (Beta 2) in Creo Tolerance Analysis powered by CETOL Technology.
where:
μ4 = fourth central moment
