Harmonic Mean and Its Confidence Interval

Calculates the harmonic mean and its confidence interval of a vector x.

Usage

hmean(
  x,
  conf.level = NA,
  sides = c("two.sided", "left", "right"),
  method = c("classic", "boot"),
  na.rm = FALSE,
  ...
)

Arguments

x: a positive numeric vector. An object which is not a vector is coerced, if possible, by as.vector().
conf.level: confidence level of the interval. If set to NA (the default), only the point estimate is returned.
sides: character string specifying the sidedness of the confidence interval (one of "two.sided" (default), "left" or "right"). See ConfidenceIntervals().
method: a vector of character strings representing the type of intervals required. The value should be any subset of the values "classic", "boot". See boot::boot.ci().
na.rm: logical, indicating whether NA values should be stripped before the computation proceeds. Defaults to FALSE.
...: further arguments are passed to the boot::boot() function. Supported arguments are type ("norm", "basic", "stud", "perc", "bca"), parallel and the number of bootstrap replicates R. If not defined those will be set to their defaults, being "basic" for type, option "boot.parallel" (and if that is not set, "no") for parallel and 999 for R.

Value

if conf.level = NA, a numeric scalar. Otherwise a named numeric vector with elements:

est: point estimate of the harmonic mean
lci: lower confidence interval bound
uci: upper confidence interval bound

Details

To compute the harmonic mean, 1/x is first calculated, before the arithmetic mean and its confidence interval are computed by lumen::meanCI(). The harmonic mean is then the reciprocal of the arithmetic mean of the reciprocals of the values. The same applies to the confidence interval.

The harmonic mean is restricted to strictly positive inputs. Non-positive values are turned into NA and therefore make the result NA unless na.rm = TRUE, in which case they are dropped. If the lower bound of the confidence interval is not greater than zero, then the confidence interval is not defined, and thus NA will be reported.

sides names the side on which the finite bound lies: "left" yields an interval bounded below, "right" one bounded above. The harmonic mean of positive values is itself positive, so the open lower side is reported as 0 rather than as NA or \(-\infty\).

Use sapply() to calculate the measures from data frame, resp. from a matrix.

References

Snedecor, G. W., Cochran, W. G. (1989) Statistical Methods, 8th ed. Ames, *IA: Iowa State University Press *

Examples


x <- runif(5)
hmean(x)
#> [1] 0.2616124

m <- matrix(runif(50), nrow = 10)
apply(m, 2, hmean)
#> [1] 0.3173872 0.5184113 0.2761854 0.2949970 0.3583152

sapply(as.data.frame(m), hmean)
#>        V1        V2        V3        V4        V5 
#> 0.3173872 0.5184113 0.2761854 0.2949970 0.3583152