How to work with of Probability and Statistical function in R

1. Probability & Statistics in R
S.Sangeetha

2. Toss Coin

3. URN Samples

4. Roll die
Extract rows that satisfy a logical expression using the subset function.

5. Equally Likely Model
• The Equally Likely Model asserts that every outcome of the sample
has the same probability.
• Sample space has n outcomes, probability is a vector of length n with
identical entries 1=n.
rep - replicate

6. Cards
A data frame, with an equally likely probs column if make space is TRUE.

7. Conditional Probability

9. Random Variables

11. Function Description
dnorm(x) normal density function (by default m=0 sd=1)
# plot standard normal curve
x <- c(1,2,3,4,5,6,7,8)
y <- dnorm(x)
plot(x, y, type='l', xlab="Normal Deviate",
ylab="Density”)
“p”: Points
“l”: Lines
“b”: Both
“h”: Histogram like (or high-density) vertical lines
“n”: No plotting

12. dbinom(x, size, prob) binomial distribution where size is the sample size
and prob is the probability of a heads (pi)
# prob of 0 to 5 heads of fair coin out of 10 flips
dbinom(0:5, 10, .5)

13. The Binomial Distribution
• distrEx package
The corresponding R function for the PMF and CDF are dbinom and pbinom, respectively.

14. Cumulative Distribution Function

15. Moment Generating Functions
• distrEx package provides an expectation operator E

16. Poisson Distribution
dpois(x, lamda)
poisson distribution with m=std=lamda
#probability of 0,1, or 2 events with lamda=4
dpois(0:2, 4)

17. Poisson Distribution

18. Continuous random variable

19. Other Useful Functions
Function Description
seq(from , to, by) generate a sequence
indices <- seq(1,10,2)
#indices is c(1, 3, 5, 7, 9)
rep(x, ntimes) repeat x n times
y <- rep(1:3, 2)
# y is c(1, 2, 3, 1, 2, 3)
cut(x, n) divide continuous variable in factor with n levels
y<-c(1,2,3,4,5)
> z<-cut(y,5)
> z
[1] (0.996,1.8] (1.8,2.6] (2.6,3.4] (3.4,4.2]
(4.2,5]

20. Cut
• x <- c(18, 42, 31, 25, 76, 22)
• x2 <- ifelse(x >= 18 & x <= 34, "18-34",
ifelse(x >= 35 & x <= 64, "35-64",
ifelse(x >= 65, "65+", NA)))
• ## [1] "18-34" "35-64" "18-34" "18-34" "65+" "18-34“
• cut(x, breaks=c(17, 34, 64, Inf), labels=c("18-34", "35-64", "65+"))
• ## [1] 18-34 35-64 18-34 18-34 65+ 18-34

21. Statistic in R

22. Function Description
mean(x, trim=0) mean of object x
# trimmed mean, removing any missing values and
5 percent of highest and lowest scores
mx <- mean(x ,trim=.05)
sd(x) standard deviation of object(x)
median(x) median
sum(x) sum

23. min(x) minimum
max(x) maximum
range(x) range
quantile(x, probs) • x is the numeric vector whose quantiles are desired
• probs is a numeric vector with probabilities in [0,1].
# 30th and 84th percentiles of x
y <- quantile(x, c(.3,.84))

24. Inter Quantile Range
IQR(x)
Package e1071
High kurtosis tend to have heavy tails, or outliers.

25. Graphs-Histogram
Main=“”-> Suppresses main title
Freq =false -> Relative frequency Histogram

26. Graphs

27. Outliers

28. Standardizing variables
scale(x, center = TRUE, scale = TRUE)

29. Bivariate Data

33. Interactive graphs
• Base plotting system, lattice package, ggplot2 package
• ggplot
• Create graphs for univariate and multivariate numerical and categorical data r.
• Generate complex plots
• Create high quality graphics
• Htmlwidgets
• Plotly
• shiny

34. References
• P. Kuhnert & B. Venables, An Introduction to R: Software for Statistical
Modeling & Computing
• J.H. Maindonald, Using R for Data Analysis and Graphics
• W.N. Venebles & D. M. Smith, An Introduction to R
• G. Jay Kerns, “Introduction to Probability and Statistics Using R”, Third
Edition”