The QGIS Standard Deviational Ellipse plugin implements the method presented in The Standard Deviational Ellipse; An Updated Tool for Spatial Description Robert S. Yuill. Geografiska Annaler. Series B, Human Geography. Vol. 53, No. 1 (1971), pp. 28-39. URL: https://www.jstor.org/stable/490885
Apparently, there are many definitions of a Standard Deviational Ellipse. CrimeStat implements a method that produces different results from the Yuill method, and this method is offered as an alternative. This method is also implemented in the R aspace package.
The calculations of the standard deviational ellipse parameters is performed in a separate thread.
The current version is 1.2.
Standard Deviational Ellipse Plugin
Standard Deviational Ellipse code repository
Standard Deviational Ellipse issues
Robert S. Yuill: The Standard Deviational Ellipse; An Updated Tool for Spatial Description
Bin Wang, Wenzhong Shi and Zelang Miao: Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space
Jianxin Gong: Clarifying the Standard Deviational Ellipse
Ned Levine: CrimeStat IV, Part II Spatial Description