Geometric mean

Calculate the geometric mean.

Usage

geometric_mean(x, na.rm = TRUE)

Arguments

x

A numeric vector

na.rm

TRUE or FALSE. If TRUE, NA values are removed prior to computation.

Value

Numeric vector

Details

The geometric mean is calculated as

$$ (\prod{x_{i}})^{\frac{1}{n}} = \sqrt[n]{x_{1} x_{2} x_{3} \cdots x_{n}} = e^{\text{arithmetic mean}(ln(x))} $$

thus is undefined for negative values (NaN) and if any value is zero (i.e. -100%) the geometric mean will result in zero.

The geometric mean is useful for data which spreads several orders of magnitude, ratios, percentages, and other scales bounded by zero. It should not be used on data which is already log transformed such as pH or decibels (db).

It's common to work with values which form a sequence of percent change (i.e. 1%, 3%, 0%, -2%, 5%, ...). The geometric mean for this sequence should be calculated on the decimal multiplier equivalent values which can be calculated by adding one to the decimal change (i.e. 1.01, 1.03, 1, 0.98, 1.05, ...). You may then subtract one from the geometric mean to convert back to the percent change.

Examples

#----------------------------------------------------------------------------
# geometric_mean() examples
#----------------------------------------------------------------------------
library(bkstat)

geometric_mean(-1)
#> [1] NaN
geometric_mean(c(1.03, 1.04, 0))
#> [1] 0
geometric_mean(c(1.02, 1.03, 1.04))
#> [1] 1.029968