F distribution

F - distribution 

F distribution is a distribution with two degrees of freedom which is usually notated as n(df1) and m(df2). 

The distribution is highly related to Chi-square distribution, also related to a gamma distribution, beta distribution ,and t distribution. 

<pdf, expected value, variance of F distribution>

<The way to interpret the graph of F distribution >

<The way to interpret F distribution table>

 

F distribution table usually exists for a=0.1, 0.05, 0.025, 0.01, 0.001

I will show two cases when a=0.1 and a=0.05

1. F table for a=0.1

2. F table for a=0.05

<Relationship between F distribution and Chi square distribution>

<Relationship between F distribution and Gamma distribution>

<Relationship between F distribution and Beta distribution>

<Relationship between F distribution and t-distribution>

<Relationship between F distribution and Normal distribution (Chi-square distribution)>

<The first Property of F distribution>

<The second property of F distribution>

<Plot and Calculation with R >

<An example I will show in R >

> curve(df(x,7,10),from=0,to=10)

> x<-seq(2.4,10)

> plot<-df(x,df1=7,df2=10)

> polygon(c(x, rev(x)), c(plot, rep(0, length(plot))),col = adjustcolor('red', alpha=0.3),border=NA)

> pf(2.41397,df1=7,df2=10)

[1] 0.9000005

> 1-pf(2.41397,df1=7,df2=10)

[1] 0.0999995