umx (version 4.20.0)

geometric_mean: Geometric Mean

Description

The Geometric mean is the nth-root of the product of n input values. Common uses include computing economic utility. That is to say, the utility of c(1, 2, 10) is $$(1 * 2 * 10)/3$$ = 6.6 not 6.3 (the arithmetic mean).

Usage

geometric_mean(x, na.rm = c(TRUE, FALSE))

Value

• Geometric mean of x

Arguments

x

A vector of values.

na.rm

remove NAs by default.

References

• https://en.wikipedia.org/wiki/Geometric_mean

See Also

Other Miscellaneous Stats Functions: FishersMethod(), SE_from_p(), harmonic_mean(), oddsratio(), reliability(), umxCov2cor(), umxHetCor(), umxParan(), umxWeightedAIC(), umx_apply(), umx_cor(), umx_means(), umx_r_test(), umx_round(), umx_scale(), umx_var(), umx

Examples

geometric_mean(c(50, 100))

# For a given sum, geometric mean is maximised with equality
geometric_mean(c(75,75))

v = c(1, 149); c(sum(v), geometric_mean(v), mean(v), median(v))
# 150.00000  12.20656  75.00000  75.00000

# Underlying logic
sqrt(50 * 100)

# Alternate form using logs
exp(mean(log(c(50 *100))))

# Reciprocal duality
1/geometric_mean(c(100, 50))
geometric_mean(c(1/100, 1/50))