#Biostatistics 070

#COMMANDS FOR PROBABILITY DISTRIBUTIONS IN R
#FOR INFORMATION ON FUNCTIONS
? dnorm()

? dt()
? dchisq()

? df()
? dbinom()

# BINOMIAL DISTRIBUTION:

# SETS UP VARIABLE X AS A RANGE 

x=seq(0,20,1)

#NUMBER OF TRIALS:
n=20
#PROBABILITY

p=0.5

dist=dbinom(x,n,p)

plot(dist,type="s")

# NORMAL DISTRIBUTION:

# SETS UP VARIABLE X AS A RANGE
x=seq(-4,4,0.1)

# SPECIFY MEAN (mu) & 

# STANDARD DEVIATION (sigma)
mu=0
sigma=1

dist=dnorm(x,mu,sigma)
plot(dist, type="p")

#STUDENT'S t DISTRIBUTION:
# SETS UP VARIABLE X AS A RANGE 

x=seq(-4,4,0.1)

# SPECIFY DEGREES OF FREEDOM

dft=1
#PLOTTING WITH LINE TYPE “1” (the letter l)

dist=dt(x,dft)

plot(dist,type="l")

# CHI-SQUARE DISTRIBUTION:

# SETS UP VARIABLE X AS A RANGE 
x=seq(0,8,0.1)
# SPECIFY DEGREES OF FREEDOM
dfchisq=5
#PLOTTING 

dist=dchisq(x,dfchisq)

plot(dist)

# F DISTRIBUTION:
# SETS UP VARIABLE X AS A RANGE 
x=seq(0,8,0.1)

# SPECIFY DEGREES OF FREEDOM
dfF1=2
dfF2=7
#PLOTTING 
dist=df(x,dfF1,dfF2)

plot(dist)

#p AND q FUNCTIONS FOR EACH DISTRIBUTION:
#PQ FUNCTIONS FOR BINOMIAL DISTRIBUTION:

n=20
p=0.50
x=5
PHI=0.95

pbinom(x,n,p)

qbinom(PHI,n,p)

#PQ FUNCTIONS FOR NORMAL DISTRIBUTION:
mu=0

sigma=1

x=1.6449
PHI=0.90
pnorm(x,mu,sigma)

qnorm(PHI,mu,sigma)

#PQ FUNCTIONS FOR STUDENT'S t DISTRIBUTION:
dft=1
x=1.6449

PHI=0.90
pt(x,dft)
qt(PHI,dft)

#PQ FUNCTIONS FOR CHISQ DISTRIBUTION:

dfchisq=1
x=1.6449
PHI=0.90
pchisq(x,dfchisq)
qchisq(PHI,dfchisq)

#PQ FUNCTIONS FOR F DISTRIBUTION:

dfF1=2
dfF2=7
x=1.6449
PHI=0.95

pf(x,dfF1,dfF2)

qf(PHI,dfF1,dfF2)

# PSEUDO-RANDOM VECTORS:
# SPECIFY VECTOR LENGTH 
m
m=1000
# SPECIFY PARAMETERS:

mu=0

sigma=1
dft=1

dfchisq=3
dfF1=2

dfF2=7

n=20

p=0.50
Knorm=rnorm(m,mu,sigma)

Kt=rt(m,dft)

Kchisq=rchisq(m,dfchisq)

KF=rf(m,dfF1,dfF2)

Kbinom=rbinom(m,n,p)



# MAKE HISTOGRAMS:

hist(Knorm)

hist(Kt)
hist(Kchisq)

hist(KF)

hist(Kbinom)