hm {greybox}

Half moment of a distribution and its derivatives.

Description

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().

Usage

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.

Details

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

Value

A complex variable is returned for the hm() and cextremity() functions, and real values are returned for ham(), asymmetry() and extremity().

Author(s)

Ivan Svetunkov, [e-mail]

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.

Examples

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