I have just submitted a new paper to be considered for publication (after review).
The new paper continues an earlier popular paper:
Why the Mode Departs from the Mean (Published, Open Access)
Here is an Abstract of the new submission.
Abstract
In a recent short communication (Shore, 2024a), we have introduced a new paradigm for sources of random variation. It helps explain why the mode occasionally departs from the mean. In essence, the new paradigm states that for any perceived random variation there are at most two sources of variation —identity instability and error. When identity is stable (there is only error variation), the allied statistical distribution is symmetric (mode equals the mean). When identity is completely random (there is only identity variation, error undefinable), mode either does not exist or resides at either end-points of the distribution support. The purpose of this communication is to explore how error is re-defined, consistent with the new paradigm. A general model for random variation is developed, comprising two additive independent random variables, averaged by a repetitiveness measure. Model’s implications are probed.
Haim Shore Blog 