Joint Moment

What is a Joint Moment?

A Joint Moment describes the values of two, or more, sets of points. Depending on the points of data, the moments may vary, yet are often defined by low-order moments when looking at probability density. For example, the first moment refers to the data set's mean. The second moment is the distribution's variance. The third moment is the skewness, or the extent to which the data is "offset" from a traditional bell curve. The fourth moment is the distribution's kurtosis, displayed often as the distribution's tail. The 0 moment encapsulates the entire probability of the distribution, a value of 1. While there are more than four moments, the fifth moment and beyond, referred to as high-order moments, are more challenging to estimate and describe.

The different moments of a probability distribution

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How does a Joint Moment work?

A Joint Moment incorporates multiple variables, rather than just one. Joint moment's are sometimes referred to as mixed moments, due to their mixed variables. Mixed moments are described with the prefix "co" as seen in the examples covariance, coskewness, and cokurtosis. In short, Joint Moments for covariance describe the degree to which random variables vary similarly.

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The Joint Moment covariance allows for an understanding of the way two variables interact with each other. Moments are integral in comparing two different variables and the ways in which their distributions overlap.