library(tigerstats)

#평균=40,표준편차=10인 정규분포에서 42보다 작을 확률
pnorm(42,mean=40,sd=1.5)

#P(Z<K)=0.9087888일 때, K의 값은?
qnorm(0.9087888, 40,1.5)

pnormGC(42,m=40, sd=1.5,region="below",graph=T)
qnormGC(0.9088,m=40, sd=1.5,region="below",graph=T)

#카이제곱 통계량이 18.307, df=10일 때 p의 값은?
pchisq(18.307, 10)

#P(chisq<K)=0.9499994일 때, K의 값은?
qchisq(0.9499994, 10)

pchisqGC(18.307,region="below",df=10,graph=T)

#t-통계량이 2.086, df=20일 때 p의 값은?
pt(2.086, 20)

#P(t<K)=0.9750018일 때, K의 값은?
qt(0.9750018, 20)

ptGC(2.086,region="below",df=20,graph=T)

#F-통계량이 6.16, df1=6, df2=4일 때 p의 값은?
pf(6.16, 6,4)

#P(F<K)=0.9499573일 때, K의 값은?
qf(0.9499573, 6, 4)

#create density curve
curve(df(x, df1 = 6, df2=4), from = 0, to = 8,
      main = 'F Distribution (df1 = 6, df2=4)',
      ylab = 'Density',
      lwd = 2)
#find upper and lower values for middle 95% of distribution
#lower95 <- qf(.025, 20)
upper95 <- qf(.95, 6,4)
upper95
#create vector of x values
x_vector <- seq(0,upper95,by=0.05)
#create vector of F density values
p_vector <- df(x_vector, df1=6, df2=4)
#fill in density plot
polygon(c(x_vector, rev(x_vector)), c(p_vector, rep(0, length(p_vector))),
        col = adjustcolor('red', alpha=0.3), border = NA)

library(sjPlot)
dist_f(p=0.05, deg.f1 = 6, deg.f2 = 4, xmax=8)