> #7.8 Milk Bacteria Example
> x<-rbind(
+ c(0,  56),
+ c(1, 104),
+ c(2,  80),
+ c(3,  62),
+ c(4,  42),
+ c(5,  27),
+ c(6,   9),
+ c(7,   9),
+ c(8,   5),
+ c(9,   3),
+ c(10,  2),
+ c(11,  1))
> 
> #Negative-binomial class probabilities from Jarvis (1989, p50)
> #note the table on page 7.2 is incorrect
> expected<-c(60.88,90.76,85.16,64.12,42.32,25.58,14.49,7.85,4.09,2.07,1.02,1.66)
> tab<-cbind(x[,2],expected)
> colnames(tab)<-c("Observed","Expected")
> rownames(tab)<-x[,1]
> tab
   Observed Expected
0        56    60.88
1       104    90.76
2        80    85.16
3        62    64.12
4        42    42.32
5        27    25.58
6         9    14.49
7         9     7.85
8         5     4.09
9         3     2.07
10        2     1.02
11        1     1.66
> 
> #totals & plot
> apply(tab,2,sum)
Observed Expected 
     400      400 
> barplot(t(tab),beside=T,legend.text=c("Observed","Expected"))
> 
> #DDR and plot
> ddr<-sqrt(4*tab[,1]+2)-sqrt(4*tab[,2]+2)
> ddr[tab[,1]==0]<-1-sqrt(4*tab[,2]+1)[tab[,1]==0]
> plot(x[,1],ddr,xlab="Category",ylab="DDR",type="n")
> points(x[,1],ddr,cex=2)
> 
> #gof stuff - note have to specify how many parameters were estimated
> #Note here attribute the estimated parameters to solving for the location/scale components to be zero
> GOF(tab,q=2,qcomps=c(1,2))
Note 2 parameters were estimated to calculate expected values
The particular component indices given zero df to compensate are:
1 2 
This information is only used to calculate partition dfs and p-values

$AndersonDarling
[1] 0.3152322

$Vr
 [1] -0.1079944  0.3685941  0.4063124 -1.2799103 -0.2240622 -1.6235069
 [7]  0.7291098 -0.2663582 -0.6055996 -0.4172515  1.0388703

$partition
           df        SS    pvalue
Location    0 0.0116628        NA
Dispersion  0 0.1358616        NA
Skewness    1 0.1650898 0.6845131
Kurtosis    1 1.6381705 0.2005767
Residual    7 4.9086275 0.6711129
Total       9 6.8594122 0.6517539

>