# Ashmans_D: A function to calculate Ashman, Bird, and Zepf's D Statistic In modes: Find the Modes and Assess the Modality of Complex and Mixture Distributions, Especially with Big Datasets

## Description

This function calculates Ashman's D, which is a measure of how well differentiated two distributions (distribution components) are. For instance, if the two distributions are identical, this statistic is zero. A good rule of thumb is that if the statistic is above ~2, there is good separation. If you suspect that your data is bimodal this can be used by replicating the suspected mixture components and checking the statistic. Alternatively, if the components are known outright this is straightforward to implement.

## Usage

 `1` ```Ashmans_D(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

Ashman, K., Bird, C., & Zepf, S. (1994). Detecting bimodality in astronomical datasets. The Astronomical Journal, 2348-2361.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```##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) Ashmans_D(mu1,mu2,sd1,sd2) ##Example 2 data<-c(rnorm(15,0,1),rnorm(21,15,3)) hist(data) Ashmans_D(0,15,1,3) ```

modes documentation built on May 30, 2017, 4:35 a.m.