B (modified geometric mean)

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Description

Computes the B index for a vector of frequencies of categories.

Usage

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B(x, na.rm = TRUE)

Arguments

x

a vector of frequencies

na.rm

if TRUE, missing values are removed. If FALSE, NA is returned if there is any NA value.

Details

According to Wilcox (1973, p. 330), and following Kaiser (1968), the B index relies on the geometric mean, but corrects it for undesirable properties. The formula for the B index is:

1 - √{1 - ≤ft(√[K]{∏_{i=1}^k \frac{f_i K}{N}}\right)^2}

Value

The value of the B statistics, which is normalised (varies between 0 and 1).

References

Wilcox, Allen R. 'Indices of Qualitative Variation and Political Measurement.' The Western Political Quarterly 26, no. 2 (1 June 1973): 325-43. doi:10.2307/446831. Kaiser, Henry F. 'A Measure of the Population Quality of Legislative Apportionment.' The American Political Science Review 62, no. 1 (March 1968): 208. doi:10.2307/1953335.

Examples

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x <- rmultinom(1, 100, rep_len(0.25, 4))
x <- as.vector(t(x))
B(x)

df <- rmultinom(10, 100, rep_len(0.25, 4))
df <- as.data.frame(t(df))
apply(df, 1, B)