R Modes Package.
Note: Please Download from CRAN repository; the links to the left are unstable. The CRAN package for using the modes package in R is: https://cran.r-project.org/web/packages/modes/index.html and the tarball itself is available from https://cran.r-project.org/src/contrib/modes_0.6.1.tar.gz
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Description
Tutorial
12 Examples of the most useful and common features of this package are included below.
Nonparametric Examples
1. Mode examples
Example 1.1
data<-c(rep(6,9),rep(3,3))
mode(data,type=1,"NULL","NULL")
[,1]
Value 6
Length 9
Example 1.2
set.seed(1246)
data<-c(rep(6,9),rep(3,9))
mode(data,type=1,"NULL","NULL")
[,1] [,2]
Value 3 6
Length 9 9
Example 1.3
set.seed(1246)
data<-c(rep(6,9),rep(3,8),rep(7,7),rep(2,6))
mode(data,type=1,"NULL",2)
[,1] [,2] [,3] [,4]
Value 6 3 7 2
Length 9 8 7 6
Example 1.4
set.seed(1246)
data<-c(rnorm(15,0,1),rnorm(21,5,1),rep(3,3))
modes(data)
[,1]
Value 0
Length 12
Example 1.5
set.seed(1246)
data<-c(rep(6,3),rep(3,3),rnorm(15,0,1))
modes(data,3,NULL,4)
modes(data,type=2,digits=1,3)
[,1] [,2] [,3] [,4]
Value "3" "6" "-0.00528877744563036" "-0.265047873213653"
Length "3" "3" "1" "1"
[,5] [,6] [,7]
Value "-0.383946266260758" "-0.503595358662098" "-0.890103993657086"
Length "1" "1" "1"
[,8] [,9] [,10]
Value "-0.902559181415477" "-0.929018190441427" "-1.51710239243673"
Length "1" "1" "1"
[,11] [,12] [,13]
Value "0.196147751721519" "0.216425886134856" "0.400936002681914"
Length "1" "1" "1"
[,14] [,15] [,16]
Value "0.461525542956227" "0.541086638435628" "1.3029586964899"
Length "1" "1" "1"
[,17]
Value "1.34537915481889"
Length "1"
Warning message:
In modes(data, 3, NULL, 4) : A single observation
is being observed as a mode.
Double check the class or inspect the data.
Alternatively, you may have specified 'nmore' too many times
for this data.
modes(data,type=2,digits=1,3)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
Value -0.9 3 6 -2 -0.5 -0.3 0.2 0.5
Length 3.0 3 3 1 1.0 1.0 2.0 2.0
Warning message:
In modes(data, type = 2, digits = 1, 3) : A single observation
is being observed as a mode.
Double check the class or inspect the data.
Alternatively, you may have specified 'nmore' too many times
for this data.
2) Other General Parametric Examples
Example 2.1
set.seed(1246)
data<-c(rnorm(15,0,1),rnorm(21,5,1))
hist(data)
bimodality_amplitude(data,TRUE)
bimodality_coefficient(data,TRUE)
bimodality_ratio(data,FALSE)
> bimodality_amplitude(data,TRUE)
[1] 0.5343913
> bimodality_coefficient(data,TRUE)
[1] 0.8894365
> bimodality_ratio(data,FALSE)
Amplitude (y)
1.413765
Example 2.2
set.seed(1246)
data<-c(rnorm(21,0,1),rnorm(21,5,1))
hist(data)
bimodality_amplitude(data,TRUE)
bimodality_coefficient(data,TRUE)
bimodality_ratio(data,FALSE)
> bimodality_amplitude(data,TRUE)
[1] 0.5569044
> bimodality_coefficient(data,TRUE)
[1] 0.880667
> bimodality_ratio(data,FALSE)
Amplitude (y)
0.9039876
3) Mixture Proportions Examples
Example 3.1
set.seed(1246)
dist1<-rnorm(21,5,2)
dist2<-dist1+11
data<-c(dist1,dist2)
hist(data)
bimodality_amplitude(data,TRUE)
bimodality_ratio(data,FALSE)
> bimodality_amplitude(data,TRUE)
[1] 0.6894354
> bimodality_ratio(data,FALSE)
Amplitude (y)
1.000229
Example 3.2
set.seed(1246)
dist1<-rnorm(21,-15,1)
dist2<-rep(dist1,3)+30
data<-c(dist1,dist2)
hist(data)
bimodality_amplitude(data,TRUE)
bimodality_ratio(data,FALSE)
> bimodality_amplitude(data,TRUE)
[1] 1
> bimodality_ratio(data,FALSE)
Amplitude (y)
2.999414
Example 3.4
dist1<-rep(7,70)
dist2<-rep(-7,70)
data<-c(dist1,dist2)
hist(data)
bimodality_ratio(data,FALSE)
> bimodality_ratio(data,FALSE)
Amplitude (y)
1
Parametric Examples
4) Replicating a two component Gaussian (normal) mixture
Example 4.1
Draw data & plot the distribution
set.seed(1246)
dist1<-rnorm(14,-5,1)
dist2<-rnorm(21,5,1)
plot(density(c(dist1,dist2)), main="Bimodal Gaussian mixture distribution")
Calculate the means and standard deviations
mu1<-mean(dist1)
mu2<-mean(dist2)
sd1<-sd(dist1)
sd2<-sd(dist2)
Apply measures
Ashmans_D(mu1,mu2,sd1,sd2)
bimodality_separation(mu1,mu2,sd1,sd2)
> Ashmans_D(mu1,mu2,sd1,sd2)
[1] 12.10559
> bimodality_separation(mu1,mu2,sd1,sd2)
[1] -3.061472
>
5) Applying to know mixture components
Example 5.1
Draw data & plot the distribution
set.seed(1246)
data<-c(rnorm(15,0,1),rnorm(21,15,3))
plot(density(c(dist1,dist2)), main="Bimodal Gaussian mixture distribution")
Apply measures
Ashmans_D(mu1,mu2,sd1,sd2)
bimodality_separation(mu1,mu2,sd1,sd2)
> Ashmans_D(mu1,mu2,sd1,sd2)
[1] 12.10559
> bimodality_separation(mu1,mu2,sd1,sd2)
[1] -3.061472
References
Ashman, K., Bird, C., & Zepf, S. (1994). Detecting bimodality in astronomical datasets. The Astronomical Journal, 2348-2361.
Ellison, A. (1987). Effect of Seed Dimorphism on the Density-Dependent Dynamics of Experimental Populations of Atriplex triangularis (Chenopodiaceae). American Journal of Botany, 74(8), 1280-1288.
Zhang, C., Mapes, B., & Soden, B. (2003). Bimodality in tropical water vapour. Quarterly Journal of the Royal Meteorological Society, 129(594), 2847-2866.
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