R语言-t分布正态分布分位数图的实例

r是用于统计分析、绘图的语言和操作环境。

r是属于gnu系统的一个*、免费、源代码开放的软件，它是一个用于统计计算和统计制图的优秀工具。

它是一套由数据操作、计算和图形展示功能整合而成的套件。

包括：有效的数据存储和处理功能，一套完整的数组（特别是矩阵）计算操作符，拥有完整体系的数据分析工具，为数据分析和显示提供的强大图形功能，一套（源自s语言）完善、简单、有效的编程语言（包括条件、循环、自定义函数、输入输出功能）。

如何用rstudio做分位数图呢？

#分位数图，画t分布密度带p值x=seq(-6,6,length=1000);y=dt(x,19)r1=-6;r2=-2.89;x2=c(r1,r1,x[x<r2&x>r1],r2,r2)y2=c(0,dt(c(r1,x[x<r2&x>r1],r2),19),0)plot(x,y,type="l",ylab="density oft(19)",xlim=c(-5,5))abline(h=0);polygon(x2,y2,col="red")title("tail probability for t(19)")text(c(-4.1,-2,5),c(0.02,-0.07),c("p-value=0.0047","t=-2.89"))#对称#x=seq(-6,6,length=1000);y=dt(x,19)r1=6;r2=2.89;x2=c(r1,r1,x[x<r2&x>r1],r2,r2)y2=c(0,dt(c(r1,x[x<r2&x>r1],r2),19),0)plot(x,y,type="l",ylab="density oft(19)",xlim=c(-5,5))abline(h=0);polygon(x2,y2,col="red")title("tail probability for t(19)")text(c(-4.1,-2,5),c(0.02,-0.07),c("p-value=0.0047","t=-2.89")) #两边#x=seq(-6,6,length=1000);y=dt(x,19)r1=-6;r2=-2.89;r3=2.89;r4=6;x2=c(r1,r1,x[x<r2&x>r1],r2,r2)y2=c(0,dt(c(r1,x[x<r2&x>r1],r2),19),0)x3=c(r3,r3,x[x<r4&x>r3],r4,r4)y3=c(0,dt(c(r3,x[x<r4&x>r3],r4),19),0)plot(x,y,type="l",ylab="density oft(19)",xlim=c(-5,5))abline(h=0);polygon(c(x2,x3),c(y2,y3),col="red");title("tail probability for t(19)")text(c(-4.1,-2.5),c(0.02,-0.007),c("p-value=0.0047","t=-2.89"))text(c(2.5,4.1),c(0.02,-0.007),c("p-value=0.9953","t=2.89"))#正态分布x=seq(-5,5,0.01)                                        #得到步长0.01的x范围plot(x,dnorm(x),type="l",xlim=c(-5,5),ylim=c(0,2),main="the normal density distribution")                 #画curve(dnorm(x,1,0.5),add=t,lty=2,col="blue")lines(x,dnorm(x,0,0.25),col="green")lines(x,dnorm(x,-2,0.5),col="orange")legend("topright",legend=paste("m=",c(0,1,0,-2),"sd=",  #m:均值 sd:方差c(1,0.5,0.25,0.5)),lwd=3,lty=c(1,2,1,1),col=c("black","blue","green","red"))#分布函数set.seed(1)x<-seq(-5,5,length.out=100)y<-pnorm(x,0,1)plot(x,y,col="red",xlim=c(-5,5),ylim=c(0,1),type="l", xaxs="i",yaxs="i",ylab='density',xlab='', main="the normal cumulative distribution")lines(x,pnorm(x,0,0.5),col="green")lines(x,pnorm(x,0,2),col="blue")lines(x,pnorm(x,-2,1),col="orange")legend("bottomright",legend=paste("m=",c(0,0,0,-2),"sd=",c(1,0.5,2,1)),lwd=1,col=c("red","green","blue","orange"))

得到的图形结果如下：

补充：r语言绘制不同*度下的卡方分布、t分布和f分布

看代码吧~

# === chi-squared distribution ===chif <- function(x, df) {  dchisq(x, df = df)}## === chi-squared distribution with df=1,2, 4, 6 and 10 ===curve(chif(x, df = 1), 0, 20, ylab = "p(x)", lwd = 2)curve(chif(x, df = 2), 0, 20, col = 2, add = t, lty = 2, lwd = 2)curve(chif(x, df = 4), 0, 20, col = 3, add = t, lty = 3, lwd = 2)curve(chif(x, df = 6), 0, 20, col = 4, add = t, lty = 4, lwd = 2)curve(chif(x, df = 10), 0, 20, col = 5, add = t, lty = 5, lwd = 2)legend("topright", legend = c("df=1", "df=2", "df=4", "df=6", "df=10"), col = 1:5, lty = 1:5, lwd = 2)## === chi-squared distribution with df=4,6 and 10 ===curve(dchisq(x, 4), 0, 20, col = 3, lty = 3, lwd = 2, ylab = "p(x)")curve(dchisq(x, 6), 0, 20, col = 4, add = t, lty = 4, lwd = 2)curve(dchisq(x, 10), 0, 20, col = 5, add = t, lty = 5, lwd = 2)legend("topright", legend = c("df=4", "df=6", "df=10"), col = 3:5, lty = 3:5, lwd = 2)### quantilescurve(dchisq(x, 10), 0, 30, col = 1, lty = 1, lwd = 2, ylab = "p(x) of chisq(10)")lines(c(qchisq(0.95, 10), qchisq(0.95, 10)), c(-0.05, dchisq(qchisq(0.95, 10), 10)), col = 2, lwd = 3,       lty = 2)qchisq(0.95,10)## ==== t ===curve(dt(x, 1), -6, 6, ylab = "p(x)", lwd = 2, ylim = c(0, 0.4))curve(dt(x, 2), -6, 6, col = 2, add = t, lwd = 2)curve(dt(x, 5), -6, 6, col = 3, add = t, lwd = 2)curve(dt(x, 10), -6, 6, col = 4, add = t, lwd = 2)curve(dnorm(x), col = 6, add = t, lwd = 2, lty = 2)legend("topright", legend = c("df=1", "df=2", "df=5", "df=10", "df=inf"), col = c(1:4, 6), lty = c(rep(1, 4), 2), lwd = 2)curve(dt(x, 4), -6, 6, col = 4, lwd = 2, ylim = c(0, 0.4), ylab = "p(x)")curve(dnorm(x), col = 6, add = t, lwd = 2, lty = 2)legend("topright", legend = c("t(4)", "n(0,1)"), col = c(4, 6), lty = c(1, 2), lwd = 2)qt(0.025,10)qt(0.975,10)## === f ==curve(df(x, 4, 1), 0, 4, ylab = "p(x)", lwd = 2, ylim = c(0, 0.8))curve(df(x, 4, 4), 0, 4, col = 2, add = t, lwd = 2)curve(df(x, 4, 10), 0, 4, col = 3, add = t, lwd = 2)curve(df(x, 4, 4000), 0, 4, col = 4, add = t, lwd = 2)legend("topright", legend = c("f(4,1)", "f(4,4)", "f(4,10)", "f(4,4000)"), col = 1:4, lwd = 2)qf(0.95,10,5)qf(0.05,5,10)1/qf(0.05,5,10)

卡方分布

t分布

f分布

#卡方分布> qchisq(0.95,5)[1] 11.0705> qchisq(0.95,10)[1] 18.30704> qchisq(0.95,15)[1] 24.99579> qchisq(0.95,20)[1] 31.41043> qchisq(0.95,25)[1] 37.65248> qchisq(0.95,30)[1] 43.77297

#t分布> qt(0.95,5)[1] 2.015048> qt(0.95,10)[1] 1.812461> qt(0.95,15)[1] 1.75305> qt(0.95,20)[1] 1.724718> qt(0.95,25)[1] 1.708141> qt(0.95,30)[1] 1.697261

> qf(0.95,10,5)[1] 4.735063> qf(0.95,5,10)[1] 3.325835> qf(0.95,5,5)[1] 5.050329> qf(0.95,10,10)[1] 2.978237

以上为个人经验，希望能给大家一个参考，也希望大家多多支持。如有错误或未考虑完全的地方，望不吝赐教。