Description Usage Arguments Details Value Author(s) References Examples
Fits three laws (exponential, power and truncated power laws) to an empirical distribution using the maximum likelihood estimators.
1 | fitting(degree.dist, nmax)
|
degree.dist |
vector of the distribution to be fitted. |
nmax |
maximum of the value of |
The fitted laws are : exponential law, power law and truncated power law.
This function plots the histogram of degree.dist
(dist.ps).
This function plots also the cumulative distributions of the empirical and three fitted laws in a log-log scale (fitting.ps).
Finally, all the parameters are exported to the file fitting.txt.
mu |
parameter of the exponential law. |
gamma |
parameter of the power law. |
alpha, beta |
parameter of the truncated power law. |
AIC |
vector containing the Akaike's criterion for the fitting of the three laws. |
S. Achard
Akaike, H. (1974) A new look at the statistical model identification IEEE Transactions on Automatic Control Vol. 19, N. 6,pages 716-723.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | data(brain)
brain<-as.matrix(brain)
# WARNING : To process only the first five regions
brain<-brain[,1:5]
n.regions<-dim(brain)[2]
#Construction of the correlation matrices for each level of the wavelet decomposition
wave.cor.list<-const.cor.list(brain, method = "modwt" ,wf = "la8", n.levels = 6,
boundary = "periodic", p.corr = 0.975)
#Construction of the adjacency matrices associated to each level of the wavelet decomposition
wave.adj.list<-const.adj.list(wave.cor.list, sup = 0.44, proc.length=dim(brain)[1])
# For scale 4
degree.dist<-rowSums(wave.adj.list[[4]])
par(cex=1.5,cex.lab=1.2,font.lab=2)
hist(degree.dist,xlab="Degree", ylab="Number of regions",main=NULL,col=1,border=8)
nmax<-50
tmp<-hist(degree.dist,breaks=c(0:nmax))
cum.dist<-1-cumsum(tmp$counts)/n.regions
# cumulative distribution of degree.dist
d<-fitting(degree.dist,nmax)
exp.trace<-exp(-d$mu*(0:nmax))
# cumulative distribution of the exponential law
power.trace<-(1:(nmax+1))^(-d$gamma+1)
# cumulative distribution of the power law
gamma.trace<-1-pgamma((0:nmax),shape=d$alpha,scale=d$beta)
# cumulative distribution of the truncated power law
par(cex=1.5,cex.lab=1.2,font.lab=2)
plot(log(1:(nmax)),log(cum.dist),pch=3,xlab="log(k)",ylab="log(cumulative distribution)")
lines(log(1:(nmax+1)),log(exp.trace),lty=3,lwd=2)
lines(log(1:(nmax+1)),log(power.trace),lty=2,lwd=2)
lines(log(1:(nmax+1)),log(gamma.trace),lty=1,lwd=2)
#text(c(0.5,0.5,0.5,0.5),c(-3,-3.5,-4,-4.5),labels=c("+ data","-- power law",
# ".. exponential law","- truncated power law"),pos=4)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.