Enjoy R!

Where to download and get help: http://cran.r-project.org/ You may also try Notepad++. Here is a link with good explanation: http://jekyll.math.byuh.edu/other/howto/notepadpp/using.shtml See  what’s  there: > ls( ) Remove everything: > rm(list=ls(all=TRUE)) Basic inputs: > a <- c(3, 5, 9, 0) > a [1] 3 5 9 0 > a[3] [1] 9 > b=3 > a+b [1] 6 8 12 3 > d<- c(1,1,1,1) > a+d [1] 4 6 10 1 > a*d [1] 3 5 9 0 > sin(a) [1] 0.1411200 -0.9589243 0.4121185 0.0000000 > a^b [1] 27 125 729 0 > a*d [1] 3 5 9 0 > seq(1,3, 0.25) [1] 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 R functions for probability distributions:

Every distribution that R handles has four functions. There is a root name, for example, the root name for the normal distribution is norm. This root is prefixed by one of the letters

p for "probability", the cumulative distribution function (c. d. f.) q for "quantile", the inverse c. d. f. d for "density", the density function (p. m.f. or p. d. f.) r for "random", a random variable having the specified distribution

Distribution Functions

Beta pbeta qbeta dbeta rbeta

Binomial pbinom qbinom dbinom rbinom

Cauchy pcauchy qcauchy dcauchy rcauchy

Chi-Square pchisq qchisq dchisq rchisq

Exponential pexp qexp dexp rexp

F pf qf df rf

Gamma pgamma qgamma dgamma rgamma

Geometric pgeom qgeom dgeom rgeom

Hyper geometric phyper qhyper dhyper rhyper

Logistic plogis qlogis dlogis rlogis

Log Normal plnorm qlnorm dlnorm rlnorm

Negative Binomial pnbinom qnbinom dnbinom rnbinom

Normal pnorm qnorm dnorm rnorm

Poisson ppois qpois dpois rpois

Student t pt qt dt rt

Studentized Range ptukey qtukey dtukey rtukey

Uniform punif qunif dunif runif

Weibull pweibull qweibull dweibull rweibull

Wilcoxon Rank Sum Statistic pwilcox qwilcox dwilcox rwilcox

Wilcoxon Signed Rank Statistic psignrank qsignrank dsignrank rsignrank

%%%% c.d.f of binomial with parameters 100 and 0.3 at 30

> pbinom(30, size=100, prob=0.3, lower.tail = TRUE) [1] 0.5491236

> pbinom(30, size=100, prob=0.3, lower.tail = FALSE)

[1] 0.4508764 %%%%%%%%%%%% perform 10,000 binomial experiments > random=rbinom(10000, 100, 0.3) > hist(random)

> hist(random, freq=FALSE)

Histogram of random

random

Frequency

15 20 25 30 35 40 45

0500

1000

1500

> hist(random, freq=FALSE, xlab="TEST", ylab=NULL, main="Today")

> hist(random, freq=FALSE) > lines(0:100, dbinom(0:100, 100, 0.3), col="red")

Histogram of random

random

Density

15 20 25 30 35 40 45

0.00

0.02

0.04

0.06

0.08

Today

TEST

15 20 25 30 35 40 45

0.00

0.02

0.04

0.06

0.08

Normal distribution: Cumulative distribution function of the normal distribution: For X~N(5, 2), is

> pnorm(5, mean=5, sd=sqrt(2))

[1] 0.5 Find such that :

> qnorm(0.95, mean=5, sd=sqrt(2))

[1] 7.326174 For standard normal

> qnorm(0.95)

[1] 1.644854

> pnorm(1.96)

[1] 0.9750021

Histogram of random

random

Density

15 20 25 30 35 40 45

0.00

0.02

0.04

0.06

0.08

Showing the effect of variance: > plot(seq(-7,7, 0.25), dnorm(seq(-7,7, 0.25),mean=0,sd=1), col="red", type="l", + xlab="", ylab="", main="Effect of variance") > lines(seq(-7,7, 0.25), dnorm(seq(-7,7, 0.25),mean=0,sd=1.5), col="blue") > lines(seq(-7,7, 0.25), dnorm(seq(-7,7, 0.25),mean=0,sd=2), col="green")

-6 -4 -2 0 2 4 6

0.0

0.1

0.2

0.3

0.4

Effect of variance