Why the Mode Departs from the Mean (Published, Open Access)

The mode of a statistical distribution occasionally departs from the mean. Why is that? A new article attempts to explain the mystery.

I have recently authored a short communication, explaining the occasional departure of the mode from the mean in terms of the new “Random Identity Paradigm”.

This article has been accepted for publication in Communications in Statistics – Theory and Methods. It is now published (Shore, online April 2024; Open Access):

Why the mode departs from the mean—a short communication.

An insightful review of the paper, by an anonymous referee, is linked in a separate post:

Review of an Accepted Paper (“Why the Mode Departs from the Mean”)

A core concept in the explanation for the departure of the mode from the mean is the new “Random Identity Paradigm”. It is associated with new terms like Identity Stability, Identity Variation, and Identity-full/less distributions. A thorough introduction to the new paradigm, and allied terms, is delivered in Appendix A of the new paper (Shore, January 2024; Open Access):

A novel approach to modeling steady-state process-time with smooth transition from repetitive to semi-repetitive to non-repetitive (memoryless) processes. January 2024. Quality and Reliability Engineering. 40(1):220-235.

See also an earlier post, referring to the latter paper:

Why the Mode Occasionally Departs from the Mean?

Some further implications of the new paradigm are explored in my four-part series at “Wiley StatsRef: Statistics Reference Online”:

Parametric and Parameter-Free Shape Moments (Stat08459)

Comment: As of writing this comment (May 10, 2024), the new article has become the most read of all articles published in the last twelve months in the host journal (CIS – Theory and Method, with 233K annual downloads/views):

Most read articles (of articles published in the last twelve months)

2 replies on “Why the Mode Departs from the Mean (Published, Open Access)”

Statistical studies led me to the Fourier transform and eventually fractal calculus. Fractals are projections of rotating articulated vectors in the complex realm. They most nearly reflect real things and processes. Why? This displays the nature of the Unified Field Theory, which operates in a similar way, based on infinitesimal torsion of space-time itself. Here is the underlying reason for “Why the Mode departs from the Mean” — which is what we observe on a macroscopic scale.

LikeLike