library(vcd)

## Warning: package 'vcd' was built under R version 3.4.4

## Loading required package: grid

data("WomenQueue",package = "vcd")
str(WomenQueue)

##  table [1:11(1d)] 1 3 4 23 25 19 18 5 1 1 ...
##  - attr(*, "dimnames")=List of 1
##   ..$ nWomen: chr [1:11] "0" "1" "2" "3" ...

Use the data set WomenQueue to:

Produce plots analogous to those shown below

barplot(WomenQueue, main="",xlab="Number of Women in queues of 10",ylab="Frequency")

Check for goodness-of-fit to the binomial distribution using the goodfit(). What do you think about these numbers?

good_fit <- goodfit(WomenQueue, type="binomial")

## Warning in goodfit(WomenQueue, type = "binomial"): size was not given,
## taken as maximum count

summary(good_fit)

## 
##   Goodness-of-fit test for binomial distribution
## 
##                       X^2 df  P(> X^2)
## Likelihood Ratio 8.650999  8 0.3725869

plot(good_fit)

Now draw the binomial distribution, which is fitted on the hanging rootogram

plot(good_fit, xlab="Counts",main = 'Rootogram')

Exercise 3.5

Create a one-way table of frequencies of counts or a matrix or data frame with frequencies in the first column and the corresponding counts in the second column, suitable for use with goodfit().

count <- 0:5
Freq <- c(129, 83, 20, 9, 5, 1)
x<-"count"
y<-"Freq"
df <-data.frame(count,Freq)
names(df) <- c(x,y)
df.tab <- xtabs(Freq ~ count, df)
head(df.tab)

## count
##   0   1   2   3   4   5 
## 129  83  20   9   5   1

Fit and plot the Poisson model for these frequencies and plot the rootogram and fitted model.

PoisModel<- goodfit(df.tab, type = "poisson")
plot(PoisModel, type = "standing", xlab="count", main = "Poisson Model")

plot(PoisModel, xlab="count", main = "Rootogram")

Fit and plot the negative binomial model for these frequencies and plot the rootogram and fitted model.

PoisModel <- goodfit(df.tab, type = "nbinomial")
plot(PoisModel, type = "standing", xlab="count", main = "Negative Binomial Model")

plot(PoisModel, xlab="count", main = "Rootogram of Negative Binomial Model")

Use the data set WomenQueue to:

Produce plots analogous to those shown below

Check for goodness-of-fit to the binomial distribution using the goodfit(). What do you think about these numbers?

Now draw the binomial distribution, which is fitted on the hanging rootogram

Exercise 3.5

Create a one-way table of frequencies of counts or a matrix or data frame with frequencies in the first column and the corresponding counts in the second column, suitable for use with goodfit().

Fit and plot the Poisson model for these frequencies and plot the rootogram and fitted model.

Fit and plot the negative binomial model for these frequencies and plot the rootogram and fitted model.

What do you conclude?

There are lot of deviations from the actual value