# B (modified geometric mean)

### Description

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

### Usage

1 |

### 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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