[R] describes the statistical analysis of the data distribution
Distribution function
Normal distribution
dnorm probability density function f (x), distribution law or PK
P norm distribution function F. (X)
qnorm inverse function F-1§ distribution function, i.e. after a given probability p, find its lower quantile
rnorm generates a random number
r<-rnorm(100,0,1)
dnorm(x,mean=0,sd=1)
pnorm(q,mean=0,sd=1)
qnorm(p,mean=0,sd=1)
rnorm(n,mean=0,sd=1)
Possion distribution
dpois(x,lambda)
ppois(q,lambda)
qpois(p,lambda)
rpois(n,lambda)
Other distribution function or distribution law
| distributed | R Software name | Additional parameters |
|---|---|---|
| binomial | binom | size, prob |
| Cauchy | cauchy | location scale |
| chi-squared | chisq | df, ncp |
| exponential | exp | rate |
| F | f | df1,df2,ncp |
| geometric | geom | prob |
| hypergeometric | hyper | m,n,k |
| log-normal | lnorm | meanlog,sdlog |
| logistic | logis | location,scale |
| normal | norm | mean,sd |
| Possion | because | lambda |
| Student’s t | t | df,ncp |
| uniform | unif | min,max |
| Weibull | weibull | shape,scale |
| beta | beta | shape1, shape2, nec |
Graph
Binomial
n<-20
p<-0.2
k<-seq(0,n)
plot(k,dbinom(k,n,p),type='h',main='Binomial distribution, n=20, p=0.2',xlab='k')
Poisson distribution
lambda<-4.0
k<-seq(0,20)
plot(k,dpois(k,lambda),type='h',main='Poisson distribution, lambda=5.5',xlab='k')
Geometric Distribution
p<-0.5
k<-seq(0,10)
plot(k,dgeom(k,p),type='h',main='Geometric distribution, p=0.5',xlab='k')
Hypergeometric distribution
N<-30
M<-10
n<-10
k<-seq(0,10)
plot(k,dhyper(k,N,M,n),type='h',main='Hypergeometric distribution,N=30, M=10, n=10',xlab='k')
Negative binomial distribution
n<-10
p<-0.5
k<-seq(0,40)
plot(k, dnbinom(k,n,p), type='h',main='Negative Binomial distribution,n=10, p=0.5',xlab='k')
Distribution
Histogram and kernel density estimation function
Student body weight histogram and kernel density estimation map, and with normal probability density function of the relative ratio
w <- c(75.0, 64.0, 47.4, 66.9, 62.2, 62.2, 58.7, 63.5, 66.6, 64.0, 57.0, 69.0, 56.9, 50.0, 72.0)
hist(w, freq=FALSE)
lines(density(w),col="blue")
x<-44:76
lines(x, dnorm(x, mean(w), sd(w)), col="red")
The results obtained are shown in:
Empirical distribution
FIG empirical distribution and corresponding distribution plot
w <- c(75.0, 64.0, 47.4, 66.9, 62.2, 62.2, 58.7, 63.5, 66.6, 64.0, 57.0, 69.0, 56.9, 50.0, 72.0)
plot(ecdf(w),verticals = TRUE, do.p = FALSE)
x<-44:78
lines(x, pnorm(x, mean(w), sd(w)))
Normal QQ FIG.
w <- c(75.0, 64.0, 47.4, 66.9, 62.2, 62.2, 58.7, 63.5, 66.6, 64.0, 57.0, 69.0, 56.9, 50.0, 72.0)
qqnorm(w); qqline(w)
Stem and Leaf
x<-c(25, 45, 50, 54, 55, 61, 64, 68, 72, 75, 75,
78, 79, 81, 83, 84, 84, 84, 85, 86, 86, 86,
87, 89, 89, 89, 90, 91, 91, 92, 100)
stem(x)
Boxplot
The two methods of data
A <- c(79.98, 80.04, 80.02, 80.04, 80.03, 80.03, 80.04,
79.97, 80.05, 80.03, 80.02, 80.00, 80.02)
B <- c(80.02, 79.94, 79.98, 79.97, 79.97, 80.03, 79.95, 79.97)
boxplot(A, B, notch=T, names=c('A', 'B'), col=c(2,3))
All in all the number five
x<-c(25, 45, 50, 54, 55, 61, 64, 68, 72, 75, 75,
78, 79, 81, 83, 84, 84, 84, 85, 86, 86, 86,
87, 89, 89, 89, 90, 91, 91, 92, 100)
fivenum(x)
