`geomean`

Geometric mean

Description

It calculates the geometric mean using a Fused-Multiply-and-Add (FMA) compensated scheme for accurate computation of floating-point product.

geomean(x)

Argument	Description
`x`	a numeric vector containing the sample observations.

If x contains any non-positive values, geomean returns NA and a warning message is displayed.

The geometric mean is a measure of central tendency, which is defined as

\[G = \sqrt[n]{x_1 x_2 \ldots x_n} = \Big(\prod_{i=1}^n x_i\Big)^{1/n}.\]

This procedure calculates the product required in the geometric mean safely using a compensated scheme as proposed by Graillat (2009).

The geometric mean of the sample, a non-negative number.

Graillat, S. (2009). Accurate floating-point product and exponentiation. IEEE Transactions on Computers 58 , 994-1000.

Oguita, T., Rump, S.M., Oishi, S. (2005). Accurate sum and dot product. SIAM Journal on Scientific Computing 26 , 1955-1988.

set.seed(149)
x <- rlnorm(1000)
mean(x)    # 1.68169
median(x)  # 0.99663
geomean(x) # 1.01688