Bimodality Separation Function

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Description

This function calculates the Bimodality Separation of a data vector. Similar to Ashman, Bird, and Zepf's D statistic ("Ashman's D"), the Bimodality Separation statistic measures how differentiated two distributions (distribution components) are. However, this statistic uses the added assumption that both are Gaussian (normal) distributions (or that the distribution is a mixture of two Gaussian (normal) components). For instance, if the two distributions are identical, this statistic is zero.

Usage

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bimodality_separation(mu1, mu2, sd1, sd2, ...)

Arguments

mu1

The mean of mode 1

mu2

The mean of mode 2

sd1

The standard deviation of mode 1

sd2

The standard deviation of mode 2

...

Pass through arguments.

References

Zhang, C., Mapes, B., & Soden, B. (2003). Bimodality in tropical water vapour. Quarterly Journal of the Royal Meteorological Society, 129(594), 2847-2866.

Examples

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##Example 1
dist1<-rnorm(15,4,1)
dist2<-rnorm(21,5,1)
hist(c(dist1,dist2))

mu1<-mean(dist1)
mu2<-mean(dist2)
sd1<-sd(dist1)
sd2<-sd(dist2)
bimodality_separation(mu1,mu2,sd1,sd2)

#Example 2
data<-c(rnorm(15,0,1),rnorm(21,15,3))
hist(data)
bimodality_separation(0,15,1,3)