常用连续型概率分布

常用连续型概率分布

概率密度函数图及R语言实现

作者：张丹(@Conan_Z)

Email: bsspirit@

Website: http://www.fens.me

日期：2012-11-26

正态分布

n=100

x <- seq(-5,5,length.out=n)

plot(x,dnorm(x,0,1),col="red",xlim=c(-5,5),ylim=c(0,1),type='l',

xaxs="i", yaxs="i",ylab='density',xlab='',

main="The Normal Density Distribution")

lines(x,dnorm(x,0,0.5),col="green")

lines(x,dnorm(x,0,2),col="blue")

lines(x,dnorm(x,-2,1),col="orange")

legend("topright",legend=paste("m=",c(0,0,0,-2)," sd=", c(1,0.5,2,1)), lwd=1, col=c("red", "green","blue","orange"))

指数分步

n=100

x<-seq(-1,2,length.out=n)

plot(x,dexp(x,0.5),col="red",xlim=c(0,2),ylim=c(0,5),type='l', xaxs="i", yaxs="i",ylab='density',xlab='',

main="The Exponential Density Distribution")

lines(x,dexp(x,1),col="green")

lines(x,dexp(x,2),col="blue")

lines(x,dexp(x,5),col="orange")

legend("topright",legend=paste("rate=",c(.5, 1, 2,5)), lwd=1, col=c("red", "green","blue","orange"))

γ（伽玛）分布

n=100

x<-seq(0,10,length.out=n)

plot(x,dgamma(x,1,2),col="red",xlim=c(0,10),ylim=c(0,2),type='l',

xaxs="i", yaxs="i",ylab='density',xlab='',

main="The Gamma Density Distribution")

lines(x,dgamma(x,2,2),col="green")

lines(x,dgamma(x,3,2),col="blue")

lines(x,dgamma(x,5,1),col="orange")

lines(x,dgamma(x,9,1),col="black")

legend("topright",legend=paste("shape=",c(1,2,3,5,9)," rate=", c(2,2,2,1,1)), lwd=1, col=c("red", "green","blue","orange","black"))

weibull分布

x <- seq(0, 2.5, length.out=1000)

plot(x, dweibull(x, .5), type="l", col="blue",xlim=c(0, 2.5),ylim=c(0, 2.5), xaxs="i", yaxs="i",ylab='density',xlab='',

main="The Weibull Density Distribution")

lines(x, dweibull(x, 1), type="l", col="red")

lines(x, dweibull(x, 1.5), type="l", col="magenta")

lines(x, dweibull(x, 5), type="l", col="green")

legend("topright", legend=paste("shape =", c(.5, 1, 1.5, 5)), lwd=1, col=c("blue", "red", "magenta", "green"))

n=100

x <- seq(-5,5,length.out=n)

plot(x,df(x,1,1,0),col="red",xlim=c(-2,2),ylim=c(-10,2),type='l',

xaxs="i", yaxs="i",ylab='density',xlab='',

main="The F Density Distribution")

lines(x,df(x,1,1,2),col="green")

lines(x,dt(x,2,2,2),col="blue")

lines(x,dt(x,2,4,2),col="orange")

legend("bottomright",legend=paste("df1=",c(1,1,2,2),"df2=",c(1,1,2,4)," ncp=", c(0,2,2,2)), lwd=1, col=c("red", "green","blue","orange"))

n=100

x <- seq(-5,5,length.out=n)

plot(x,dt(x,1,0),col="red",xlim=c(-5,5),ylim=c(0,0.5),type='l',

xaxs="i", yaxs="i",ylab='density',xlab='',

main="The T Density Distribution")

lines(x,dt(x,5,0),col="green")

lines(x,dt(x,5,2),col="blue")

lines(x,dt(x,50,2),col="orange")

legend("topleft",legend=paste("df=",c(1,5,5,50)," ncp=", c(0,0,2,2)), lwd=1, col=c("red", "green","blue","orange"))