Which statistical parameter is NOT part of the common four used to measure distributions?

The correct choice highlights excess kurtosis, which is not considered one of the common statistical parameters used to measure distributions. The common four parameters typically include mean, variance, skewness, and kurtosis, which provide a comprehensive overview of a distribution's shape, center, and spread.

The mean represents the average of the data, providing a measure of central tendency. Skewness quantifies the asymmetry of the distribution, indicating whether it leans towards the left or right. Kurtosis measures the "tailedness" of the distribution, giving insights into the presence of outliers and the sharpness of the peak. Excess kurtosis is a more specialized measure that derives from kurtosis and is used to identify how much the kurtosis deviates from that of a normal distribution. While it can provide valuable information, it is derived from the basic kurtosis statistic and is therefore not one of the primary parameters commonly referenced when describing distributions.

The distinction lies in how excess kurtosis is used in practice; it's more of an adjustment or refinement of the basic kurtosis measure rather than a standard distribution descriptor on its own. Understanding these foundational parameters helps in grasping the broader characteristics of data distributions.