R: Geometric mean

geomean {fastmatrix} | R Documentation

## Geometric mean

### Description

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

### Usage

    geomean(x)

### Arguments

`x` | a numeric vector containing the sample observations.

### Details

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 = √[n]{x_1 x_2 … x_n} = \Big(∏_{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).

### Value

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

### References

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.

### See Also

`mean`, `median`.

### Examples

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

[Package fastmatrix version 0.4 Index]