hm function

Half moment of a distribution and its derivatives.

hm() function estimates half moment from some predefined constant C. ham() estimates the Half Absolute Moment. asymmetry()

function returns Asymmetry coefficient, while extremity()

returns the coefficient of Extremity, both based on hm(). Finally, cextremity() returns the Complex Extremity coefficient, based on hm().

hm(x, C = mean(x, na.rm = TRUE), ...)

ham(x, C = mean(x, na.rm = TRUE), ...)

asymmetry(x, C = mean(x, na.rm = TRUE), ...)

extremity(x, C = mean(x, na.rm = TRUE), ...)

cextremity(x, C = mean(x, na.rm = TRUE), ...)

Arguments

• x: A variable based on which HM is estimated.
• C: Centring parameter.
• ...: Other parameters passed to mean function.

Returns

A complex variable is returned for the hm() and cextremity()

functions, and real values are returned for ham(), asymmetry() and extremity().

Details

NA values of x are excluded on the first step of calculation.

Examples

x <- rnorm(100,0,1)
hm(x)
ham(x)
asymmetry(x)
extremity(x)
cextremity(x)

References

• Svetunkov I., Kourentzes N., Svetunkov S. "Half Central Moment for Data Analysis". Working Paper of Department of Management Science, Lancaster University, 2023:3, 1–21.

Author(s)

Ivan Svetunkov, ivan@svetunkov.com