Understanding a Quantile-Quantile Plot [duplicate]

Question

I must have generated at least 5 Q-Q plots until now when trying to fit my data into a known distribution but I just noticed something that I could not understand. In the figure shown below, from what I've read from the wiki, X-axis is supposed to read "Negative Binomial Theoretical Quantiles" and Y-axis is supposed to read "Data quantiles". Agreed that this makes perfect sense. But when I looked at the figure, the X and Y axis go beyond 100 but how can there be quantiles beyond 100? What do they mean if they exist? Or is this graph produced by the qqplot of R totally different? Can someone help me understand this?

The way I was generating this data was using the following script:

library(MASS)

# Define the data
data <- c(67, 81, 93, 65, 18, 44, 31, 103, 64, 19, 27, 57, 63, 25, 22, 150,
          31, 58, 93, 6, 86, 43, 17, 9, 78, 23, 75, 28, 37, 23, 108, 14, 137,
          69, 58, 81, 62, 25, 54, 57, 65, 72, 17, 22, 170, 95, 38, 33, 34, 68, 
          38, 117, 28, 17, 19, 25, 24, 15, 103, 31, 33, 77, 38, 8, 48, 32, 48, 
          26, 63, 16, 70, 87, 31, 36, 31, 38, 91, 117, 16, 40, 7, 26, 15, 89, 
          67, 7, 39, 33, 58)

# Fit the data to a model
params = fitdistr(data, "Negative Binomial")

#using the answer from params create a set of theoretical values
plot(qnbinom(ppoints(data), size=2.3539444, mu=50.7752809), sort(data))
abline(0,1)

Answer 1

I think R is doing perfectly what you want it to do.

You are plotting:

x = qnbinom(ppoints(data), size=2.3539444, mu=50.7752809)

which is:

[1] 3 5 7 9 10 11 12 13 14 15 16 17 18 19 20 [16] 21 21 22 23 24 25 25 26 27 28 28 29 30 31 31 [31] 32 33 34 35 35 36 37 38 39 39 40 41 42 43 44 [46] 45 45 46 47 48 49 50 51 52 53 54 55 56 57 59 [61] 60 61 62 63 65 66 68 69 71 72 74 76 77 79 81 [76] 84 86 89 91 94 97 101 105 110 116 123 132 146 175

with respect to

y = sort(data)

which is:

[1] 6 7 7 8 9 14 15 15 16 16 17 17 17 18 19 [16] 19 22 22 23 23 24 25 25 25 26 26 27 28 28 31 [31] 31 31 31 31 32 33 33 33 34 36 37 38 38 38 38 [46] 39 40 43 44 48 48 54 57 57 58 58 58 62 63 63 [61] 64 65 65 67 67 68 69 70 72 75 77 78 81 81 86 [76] 87 89 91 93 93 95 103 103 108 117 117 137 150 170

Therefore, you have 100+ values on both the axis. If you want to plot quantiles, you need to tell R to do so by doing this:

plot(pnbinom(sort(data), size=2.3539444, mu=50.7752809), ppoints(data))