B: B (modified geometric mean)
In qualvar: Implements Indices of Qualitative Variation Proposed by Wilcox (1973)

Description Usage Arguments Details Value References Examples

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

1	B(x, na.rm = TRUE)

`x`	a vector of frequencies
`na.rm`	if TRUE, missing values are removed. If FALSE, NA is returned if there is any NA value.

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}

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

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.

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)