正态分布N(μ,σ2)

正态分布的形态如图。

library(ggplot2)
library(reshape2)
library(dplyr)
#产生分布数据
set.seed(123)
data_norm<-data.frame(x1 = rnorm(n = 200, m = 0, sd = 1),
                      x2 = rnorm(n = 200, m = 0, sd = sqrt(2)),
                      x3 = rnorm(n = 200, m = 0, sd = sqrt(0.5)),
                      x4 = rnorm(n = 200, m = 1, sd = 1),
                      x5 = rnorm(n = 200, m = -1, sd =1)
)
data_norm_long<-melt(data_norm)
ggplot(data = data_norm_long, aes(x = value, colour = variable))+
  geom_density()+

  ggtitle

("正态分布密度函数")

正态分布可以衍生出如下的分布。

1.1.2 卡方分布

若Zi∼ i.i.dN(0,1)

set.seed(123)
data_chisq<-data.frame(x1 = rchisq(200, 10, ncp = 0),
                       x2 = rchisq(200, 50, ncp =0),
                       x3 = rchisq(200, 100, ncp = 0))
data_chisq_long<-melt(data_chisq)

## No id variables; using all as measure variables

ggplot(data = data_chisq_long, aes(x = value, colour = variable))+
  geom_density()+
  ggtitle

("卡方分布密度函数")

1.1.3t−

分布

1.1.4F−

分布

set.seed(123)
data_f<-data.frame(x1 = rf(200,df1 = 10, df2 = 10, ncp = 0),
                       x2 = rf(200,df1 = 5, df2 = 3, ncp =0),
                       x3 = rf(200, df1 = 3, df2 = 5, ncp = 0))
data_f_long<-melt(data_f)

## No id variables; using all as measure variables

ggplot(data = data_f_long, aes(x = value, colour = variable))+
  geom_density()+
  ggtitle

("F-分布密度函数")

1.1.5Wishart

分布

set.seed(123)
data_binom<-data.frame(x1 = rbinom(n = 1000, size = 10, prob = 0.6),
                      x2 = rbinom(n = 1000, size = 50, prob = 0.6),
                      x3 = rbinom(n = 1000, size = 100, prob = 0.6),
                      x4 = rbinom(n = 1000, size = 500, prob = 0.6))

data_binom_long<-melt(data_binom)
ggplot(data = data_binom_long, aes(x = value, colour = variable))+
  geom_density()+

  ggtitle

("二项分布概率分布图")

1.2.3 负二项(NegativeBinomial

)分布

负二项分布。

1.2.4 几何(Geometric

)分布

1.2.5 泊松(Poission

)分布

1.3 指数分布族及其相互联系

1.3.1 指数分布族