ベータ分布
# ベータ分布 x <- seq( 0, 1, 0.1 ) curve( dbeta( x, 0.5, 0.5 ), col="blue", from=0, to=1 ) curve( dbeta( x, 2, 2 ), col="green", add=TRUE ) curve( dbeta( x, 5, 1 ), col="red", add=TRUE ) curve( dbeta( x, 1, 5 ), col="yellow", add=TRUE )
ガンマ分布
# ガンマ分布 x <- seq( 0, 10, 0.1 ) curve( dgamma( x, shape=0.5 ), col="blue", from=0, to=10 ) curve( dgamma( x, shape=0.5, scale=2 ), col="green", add=TRUE ) curve( dgamma( x, shape=1 ), col="yellow", add=TRUE ) curve( dgamma( x, shape=3 ), col="pink", add=TRUE ) curve( dgamma( x, shape=5 ), col="red", add=TRUE )
カイ二乗分布
x <- seq( 0, 10, 0.1 ) test_df <- 1 curve( dchisq( x, test_df ), col="red", lty="longdash", add=TRUE ) test_df <- 3 curve( dchisq( x, test_df ), col="blue", lty="longdash", add=TRUE )
指数分布
x <- seq( 0, 10, 0.1 ) curve( dexp( x ), col="red", lty="longdash", from=0,to=10)
二項分布(ベルヌーイ分布)
http://d.hatena.ne.jp/HiRos/20060514/1147596737
par(ann=F) #軸と全体のタイトルを描かない #plot(1:50,dbinom(1:50, 5, p=0.5),type="l",ylim=c(0,0.3),col=1) #par(new=T) #上書きの指定 plot(1:50,dbinom(1:50, 10, p=0.5),type="l",ylim=c(0,0.3),col=2) par(new=T) #上書きの指定 plot(1:50,dbinom(1:50, 20, p=0.5),type="l",ylim=c(0,0.3),col=3) par(new=T) #上書きの指定 plot(1:50,dbinom(1:50, 30, p=0.5),type="l",ylim=c(0,0.3),col=4) par(new=T) #上書きの指定 plot(1:50,dbinom(1:50, 40, p=0.5),type="l",ylim=c(0,0.3),col=5) par(new=T) #上書きの指定 plot(1:50,dbinom(1:50, 50, p=0.5),type="l",ylim=c(0,0.3),col=6) grid()
ポアソン分布
# ポアソン分布 x <- seq( 0, 20, 1 ) plot( dpois( x, lambda=1 ), col="blue", type="b", ylim=c( 0, 0.5 ) ) par( new=TRUE ) plot( dpois( x, lambda=3 ), col="yellow", type="b", ylim=c( 0, 0.5 ) ) par( new=TRUE ) plot( dpois( x, lambda=5 ), col="red", type="b", ylim=c( 0, 0.5 ) ) par( new=TRUE ) plot( dpois( x, lambda=10 ), col="pink", type="b", ylim=c( 0, 0.5 ) ) par( new=TRUE ) plot( dpois( x, lambda=15 ), col="green", type="b", ylim=c( 0, 0.5 ) )
ガウス分布(正規分布)
http://qiita.com/HirofumiYashima/items/69c08eba285cc278a5b5
x<-0:60 curve(dnorm(x,30,5), 0, 60,col="green") curve(dnorm(x,30,10), 0, 60,col="red",add=T) curve(dnorm(x,15,10), 0, 60,col="blue",add=T) curve(dnorm(x,30,5), 0, 60,col="green",add=T)
ディリクレ分布
http://www.singularpoint.org/blog/math/stat/dirichlet-distribution-3/
3次元
plot.dirichlet <- function(x){ # x must be Nx3 matrix!! X <- x[,2]-x[,1] Y <- x[,3] par(xaxt="n") par(yaxt="n") par(bty="n") par(mar=rep(0,4)) plot(X,Y,xlim=c(-1.2,1.2),ylim=c(-0.2,1.2),xlab="",ylab="",pch=20,cex=0.7) lines(c(-1,1,0,-1),c(0,0,1,0),col="gray") text(-1,0,"x1"); text(1,0,"x2"); text(0,1,"x3") alpha <- attr(x,"alpha") stralpha <- paste("a1=",alpha[1],"\na2=",alpha[2],"\na3=",alpha[3],sep="") text(-0.8,0.8,stralpha) print(alpha) symbols(-1,0,circles=0.08*sqrt(alpha[1]),inches=F,add=T) symbols(1,0,circles=0.08*sqrt(alpha[2]),inches=F,add=T) symbols(0,1,circles=0.08*sqrt(alpha[3]),inches=F,add=T) } rdirichlet <- function(N,alpha){ d <- length(alpha) res <- matrix(0,N,d) for( i in 1:d ){ res[,i] <- rgamma(N,alpha[i]) } res <- res / rowSums(res) class(res) <- "dirichlet" attr(res,"alpha") <- alpha res } alphas <- list(c(1,1,1),c(3,2,1),c(6,2,1)) scale <- c(0.1,1,8) par(mfrow=c(3,3)) for(alpha in alphas){ for(s in scale){ plot(rdirichlet(1000,s*alpha)) } }
