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normal_distribution

Please read Normal Distribution at Wikipedia.org first.

좌우대칭이며 asymtotic한 분포를 이루는 것을 정상분포라고 한다. 수학적으로 정상분포는 아래와 같이 정의된다.

\begin{equation} 
\displaystyle P(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} * e^{\frac{-(x - \mu)^2}{2 \sigma^2}} 
\end{equation}

위에서 $\pi$$e$ 는 각각 $\pi = 3.1416, e=2.7183 $으로 상수

특히 평균이 0 이고 그 표준편차가 1인 정상분포를 표준정상분포라고 한다.

표준정규분포 table
https://www.mathsisfun.com/data/standard-normal-distribution-table.html

set.seed(3000)
xseq<-seq(-4,4,.01)
densities<-dnorm(xseq, 0,1)
cumulative<-pnorm(xseq, 0, 1)
randomdeviates<-rnorm(1000,0,1)
 
# par(mfrow=c(1,3), mar=c(3,4,4,2))

plot(xseq, densities, col="darkgreen",
   xlab="", ylab="Density", type="l", lwd=2, cex=2, 
   main="PDF of Standard Normal", cex.axis=.8)

plot(xseq, cumulative, col="darkorange", 
   xlab="", ylab="Cumulative Probability",type="l",lwd=2, cex=2, 
   main="CDF of Standard Normal", cex.axis=.8)

hist(randomdeviates, main="Random draws from Std Normal", 
   cex.axis=.8, xlim=c(-4,4))
xseq<-seq(-4,4,.01)
y<-2*xseq + rnorm(length(xseq),0,5.5)
hist(y, prob=TRUE, ylim=c(0,.06), breaks=20)
curve(dnorm(x, mean(y), sd(y)), add=TRUE, col="darkblue", lwd=2)
normal_distribution.txt · Last modified: 2019/09/24 13:04 by hkimscil