I am attempting to identify possible outliers in data which is skewed to the left and I assume it is Poisson distributed. I am a novice in all things statistics, and the following may be utterly erroneous. However, I am eager to learn.

My actual data is shown below as the vector parktimes, (n=5222). It is the results of a survey where respondents answered how long it took them (in minutes) to park their car in a postal code area in Helsinki, Finland. Respondents could answer for multiple postal code areas at the same time, leaving the data with some identical timestamps with different values for different postal code areas. Most people reported finding a parking place almost instantaneously, making the data skewed to the left. The allowed sequence here was 0-99, but 99 minutes to find a parking place in Helsinki seems unbelivable and yet someone answered with that value for multiple postal code areas. I would like to find a statistical solution to remove these improbable values if they are indeed outliers. The code below does not provide the exact timestamps to be more concise, substituting to the index.

I am attempting to identify possible outliers in data which is skewed to the right and I assume it is Poisson distributed. I am a novice in all things statistics, and the following may be utterly erroneous. However, I am eager to learn.

My actual data is shown below as the vector parktimes, (n=5222). It is the results of a survey where respondents answered how long it took them (in minutes) to park their car in a postal code area in Helsinki, Finland. Respondents could answer for multiple postal code areas at the same time, leaving the data with some identical timestamps with different values for different postal code areas. Most people reported finding a parking place almost instantaneously, making the data skewed to the right. The allowed sequence here was 0-99, but 99 minutes to find a parking place in Helsinki seems unbelivable and yet someone answered with that value for multiple postal code areas. I would like to find a statistical solution to remove these improbable values if they are indeed outliers. The code below does not provide the exact timestamps to be more concise, substituting to the index.

Here is a histogram of parktime values with ggplot: ggplot(thesisdata, aes(parktime)) + geom_histogram(color = "black", binwidth = 5)

library(ggplot2)
library(data.table)
library(outliers)

parktimes <- c(99,5,0,1,10,99,99,1,1,3,1,1,2,5,2,2,2,5,10,5,2,2,0,1,1,1,5,3,5,5,
               1,0,0,5,1,0,0,2,2,0,5,10,1,1,1,5,5,3,10,1,1,1,1,0,10,2,10,7,10,7,
               3,3,13,1,3,1,1,1,4,4,1,2,3,1,1,1,1,1,1,2,1,1,2,3,0,7,8,3,3,3,5,4,
               25,0,10,0,10,6,3,0,0,1,2,1,0,0,0,0,0,0,3,1,0,1,2,1,0,1,5,5,5,3,0,
               0,0,0,2,1,3,0,1,5,5,5,2,0,2,0,5,15,3,4,3,4,2,5,1,10,10,2,0,1,1,1,
               0,0,1,0,10,5,15,1,10,0,0,2,1,5,1,1,2,2,3,1,1,1,1,4,4,1,3,3,1,3,1,
               2,1,0,1,2,2,5,1,2,1,3,5,1,1,1,1,5,4,5,2,15,15,2,5,2,5,8,2,8,5,5,2,
               0,1,3,2,1,1,1,1,1,1,1,1,10,3,1,8,10,10,12,5,5,3,6,4,2,1,3,2,0,0,1,
               3,1,1,1,1,2,1,3,1,1,2,1,1,3,1,1,1,3,2,1,1,2,2,1,4,1,1,1,1,2,1,2,3,
               4,1,2,1,2,10,1,0,0,3,3,10,1,4,0,2,5,5,1,4,0,5,1,1,1,3,0,1,5,1,1,1,
               1,1,1,5,5,5,5,5,10,20,1,1,1,0,0,0,0,1,0,2,0,2,2,2,0,1,1,1,2,2,2,0,
               1,0,1,2,1,5,0,0,10,1,2,1,2,2,3,2,3,1,1,2,5,2,1,5,5,2,10,2,4,0,5,0,
               1,1,5,1,2,5,1,1,3,4,1,6,6,5,2,10,10,10,60,7,1,15,10,0,5,15,1,0,2,
               0,0,0,2,1,2,3,3,2,2,3,3,2,3,1,3,5,1,2,1,3,10,1,1,1,1,5,3,1,6,12,5,
               7,6,5,2,0,3,1,5,10,30,45,45,30,45,0,0,0,0,5,5,0,3,5,2,5,10,10,2,5,
               10,2,1,30,5,2,2,7,1,1,2,4,5,5,1,1,1,5,2,2,2,2,1,5,0,1,3,5,5,1,2,
               15,10,0,1,10,8,10,25,5,10,5,12,20,7,12,2,5,2,10,3,10,5,5,5,5,5,7,
               3,7,3,6,9,7,1,1,10,10,1,1,1,1,2,1,15,30,1,10,5,20,1,10,1,35,10,0,
               5,25,35,10,1,5,5,10,20,5,5,5,10,10,15,2,2,1,1,1,1,1,3,5,5,5,1,1,5,
               10,10,15,15,25,20,5,15,5,0,5,5,2,5,3,10,2,5,5,1,15,8,4,6,5,15,20,
               20,20,15,15,15,30,15,10,5,5,10,10,10,10,5,5,0,10,1,5,1,2,0,2,2,5,
               10,15,3,15,3,4,3,2,1,3,4,5,4,2,10,1,1,1,1,5,1,10,5,5,10,5,1,5,7,
               10,10,5,10,5,1,2,15,10,1,10,10,15,10,10,5,2,2,2,5,5,10,5,5,2,5,5,
               2,5,10,10,20,5,1,2,2,5,2,5,1,1,15,10,20,15,4,15,15,5,15,5,0,5,1,0,
               0,5,6,7,1,3,2,3,2,0,10,15,10,10,3,30,10,30,5,10,20,10,0,1,10,1,2,
               2,1,1,0,1,10,0,10,15,5,5,10,5,8,4,10,10,3,3,5,5,1,4,0,15,2,10,10,
               2,2,10,2,5,10,1,1,1,1,1,2,2,1,1,1,2,1,1,2,2,8,4,5,1,3,5,10,1,2,1,
               2,1,0,1,0,8,10,3,15,0,0,0,1,2,0,1,0,5,2,10,5,2,10,5,1,1,0,2,5,1,1,
               1,3,2,3,2,2,6,9,9,9,8,2,9,10,5,10,1,15,10,4,5,5,5,1,7,1,10,2,2,8,
               2,2,7,1,1,10,2,8,10,2,5,5,4,3,5,5,8,6,8,4,2,10,15,4,8,3,6,5,5,6,0,
               1,10,15,10,3,5,1,8,10,7,1,1,2,5,10,10,15,0,2,5,5,5,10,3,5,1,4,1,1,
               14,24,5,5,15,3,0,5,0,5,5,6,0,1,2,1,1,4,1,10,2,5,1,1,5,8,5,10,19,0,
               3,5,2,5,0,2,2,5,1,2,2,5,1,2,2,1,5,2,2,1,1,5,15,1,1,1,5,1,1,7,5,3,
               5,1,10,1,1,2,4,1,1,2,4,2,1,0,1,2,1,10,5,10,3,15,1,1,15,5,10,1,1,
               1,10,20,20,5,1,10,15,1,10,5,1,5,5,5,5,5,20,20,5,1,5,5,10,5,5,20,
               5,15,15,10,2,0,0,3,2,5,1,2,1,0,3,0,5,1,1,1,5,1,1,5,10,10,0,1,1,1,
               1,5,5,10,5,5,1,8,10,10,10,2,3,5,3,15,3,5,0,0,0,1,1,1,1,0,1,1,1,1,
               1,1,1,1,0,1,2,1,1,1,1,0,1,1,1,10,15,10,10,10,20,5,3,1,7,7,5,20,1,
               2,5,5,5,5,0,7,1,5,1,1,1,1,1,1,5,1,3,1,3,2,2,5,0,45,5,10,10,5,10,5,
               1,2,5,2,5,2,1,1,5,2,15,20,10,35,5,5,5,5,10,20,15,15,1,2,5,5,2,2,3,
               5,1,1,10,10,1,1,1,0,2,3,7,2,1,2,2,1,2,3,4,2,1,28,20,1,5,5,8,2,0,0,
               3,8,1,3,2,15,15,15,8,4,20,0,2,2,5,1,1,5,7,5,0,5,1,15,2,2,12,10,6,
               15,0,2,4,5,5,10,1,1,1,1,2,6,2,1,0,1,3,3,5,3,6,8,2,60,90,15,3,10,1,
               5,3,1,6,1,2,2,7,3,3,15,25,10,5,10,8,7,1,1,1,5,3,5,1,2,5,0,1,2,1,2,
               1,1,1,1,5,2,25,20,0,0,4,1,5,1,15,10,1,1,3,1,1,5,6,5,1,14,15,6,15,
               8,7,1,4,8,5,2,1,0,1,1,1,2,6,3,5,5,2,8,4,1,10,5,4,8,3,3,3,1,3,2,1,
               2,3,1,2,6,3,4,6,2,8,1,5,5,1,2,6,1,3,1,2,0,1,5,3,1,3,5,3,5,7,2,5,
               15,2,2,5,1,3,5,7,10,5,5,10,10,10,5,2,10,7,20,2,5,10,5,2,2,4,3,5,
               2,1,10,2,5,20,5,20,5,1,0,0,2,2,1,5,30,99,10,1,5,10,10,5,2,10,1,5,
               3,2,10,4,1,5,5,2,10,5,1,2,10,4,5,3,2,2,1,0,2,55,0,3,10,3,20,5,20,
               5,5,3,5,5,5,3,1,5,10,10,5,1,10,0,2,5,1,2,20,5,2,10,5,5,8,1,5,10,2,
               5,1,3,1,2,3,5,1,1,5,5,20,5,5,15,1,5,1,5,1,5,99,99,20,99,99,99,99,
               2,2,2,1,2,3,1,2,2,1,2,1,2,1,1,2,2,2,1,2,1,1,1,1,1,1,1,1,4,1,1,1,
               2,2,3,2,3,2,1,2,3,2,2,2,2,5,2,5,5,3,2,3,2,3,3,5,2,5,5,1,1,1,1,3,2,
               2,3,3,2,10,5,1,3,3,0,2,10,5,2,2,3,2,5,3,2,15,5,7,10,1,5,5,2,2,3,2,
               2,10,10,15,2,5,15,5,10,6,3,5,2,5,5,5,8,4,4,5,5,4,2,2,5,2,5,5,0,5,
               2,5,5,0,0,0,5,10,5,10,1,5,5,1,1,3,20,20,0,0,3,0,2,1,2,1,1,2,1,1,8,
               2,2,5,5,0,3,20,6,1,2,4,1,15,2,4,5,5,2,5,10,5,1,1,1,3,2,1,2,3,4,6,
               5,10,5,5,2,10,10,10,10,10,10,0,10,10,5,10,10,5,5,5,10,10,10,5,1,1,
               3,10,5,5,1,1,0,0,2,10,10,5,5,5,2,2,5,2,10,5,10,1,10,3,2,1,3,2,3,3,
               5,1,1,2,6,3,5,5,10,5,3,5,5,10,5,4,5,3,3,1,2,1,3,5,1,1,1,1,1,2,2,5,
               6,2,4,2,2,2,5,10,2,2,3,3,2,1,2,2,4,2,1,5,10,5,1,1,3,0,5,3,5,5,1,2,
               2,5,3,1,10,2,5,3,10,10,3,10,5,2,3,10,0,2,3,2,1,0,10,2,0,1,2,4,2,2,
               5,2,7,0,0,5,7,7,5,1,5,10,5,1,3,4,6,5,2,15,5,4,10,3,2,10,3,3,4,10,
               2,8,5,0,2,1,1,3,3,1,1,1,1,1,1,2,1,3,1,1,10,2,1,1,0,1,0,10,30,5,15,
               5,5,10,5,5,5,5,1,0,0,0,7,1,5,5,2,1,2,5,20,30,15,15,1,0,0,0,0,2,5,
               0,0,0,3,0,0,2,5,0,0,4,0,1,2,3,0,4,3,1,1,3,20,5,5,10,10,15,15,10,5,
               3,1,4,10,10,2,10,2,1,5,5,2,2,2,1,1,1,1,1,3,2,2,3,1,7,1,1,3,1,1,3,
               3,2,5,2,2,5,5,2,1,3,1,1,1,2,5,5,1,10,2,3,5,1,5,10,0,5,5,0,0,3,3,1,
               1,1,15,3,15,2,2,5,1,5,0,1,1,2,2,1,4,5,1,3,2,10,3,5,7,10,3,3,3,4,3,
               2,2,0,0,1,1,4,1,3,1,1,3,5,1,10,15,3,3,1,1,5,5,2,10,2,5,5,7,5,8,7,
               6,4,5,4,4,2,8,10,9,15,8,5,0,0,2,5,0,5,1,3,2,5,20,10,30,10,30,15,
               10,15,15,10,10,10,10,5,15,1,1,2,0,1,4,5,5,0,2,5,4,1,2,0,0,1,2,1,5,
               6,1,1,3,1,1,1,1,3,5,10,5,5,2,5,0,1,3,0,3,5,5,15,10,10,0,5,10,5,2,
               10,5,2,10,5,2,5,10,5,1,20,5,15,5,5,5,5,5,5,5,10,10,5,5,5,5,5,10,5,
               0,0,10,10,5,5,1,25,5,1,1,5,1,2,1,1,1,2,3,10,1,30,10,20,10,20,5,15,
               10,10,15,25,15,1,0,7,2,1,0,3,3,4,15,5,15,10,3,10,5,3,2,1,1,3,1,3,
               25,0,10,5,7,5,20,10,18,20,5,2,1,1,1,1,1,1,2,2,5,2,2,5,5,10,5,10,10,
               3,2,1,1,8,5,2,2,5,5,5,1,5,5,2,15,0,0,2,10,5,1,1,2,0,5,1,5,5,5,2,10,
               5,0,5,5,1,4,1,0,4,0,3,4,1,1,0,0,3,5,1,2,1,10,5,5,2,2,3,0,20,2,5,1,0,
               3,1,5,5,15,5,5,5,2,0,3,3,0,0,5,5,5,1,2,3,1,10,10,1,1,3,1,0,5,0,10,5,
               10,10,10,0,2,3,2,0,10,2,15,2,6,2,10,5,2,3,10,3,5,3,3,5,3,5,4,3,10,5,
               5,5,10,2,4,5,6,8,5,5,4,2,15,4,15,5,10,5,5,2,1,1,1,2,3,2,3,4,5,0,10,
               15,5,5,1,3,15,1,10,3,1,10,5,5,5,3,7,8,1,10,3,3,0,0,7,15,15,5,3,15,
               2,10,1,7,5,20,2,10,5,1,1,1,2,1,5,15,15,5,1,5,7,9,3,2,5,5,15,10,20,
               0,20,25,5,15,10,2,3,2,2,5,2,1,5,5,6,6,1,1,3,1,1,3,3,10,2,20,20,5,5,
               4,0,30,20,5,15,0,10,10,1,6,3,1,2,2,10,2,1,1,1,0,10,2,2,5,5,4,5,16,
               2,1,10,30,15,5,3,2,10,10,1,3,1,3,2,2,10,2,1,3,1,1,1,1,3,3,5,7,5,3,
               10,5,1,10,2,2,1,1,5,1,2,3,2,2,2,5,1,1,1,10,2,1,1,1,3,1,6,1,3,5,1,
               3,10,10,0,0,0,0,0,15,10,10,15,1,7,3,5,5,1,5,10,6,2,4,2,2,1,1,4,2,
               1,2,4,1,3,3,1,1,1,2,1,2,2,2,4,1,1,1,2,2,1,2,1,2,4,4,2,1,8,3,1,3,2,
               5,5,2,2,4,3,3,1,1,1,2,1,2,2,1,2,3,2,2,5,0,0,0,3,5,1,1,1,1,2,2,5,5,
               5,0,4,1,1,5,10,5,5,3,1,3,3,4,5,1,3,2,3,3,3,2,3,2,4,5,3,5,2,5,5,6,1,
               3,7,4,30,3,1,1,3,15,10,2,1,5,1,1,2,1,3,1,1,2,3,1,1,1,1,1,2,1,1,10,
               2,2,2,2,5,1,25,30,10,3,15,5,5,30,20,20,40,35,20,10,5,0,5,2,15,20,
               2,7,10,2,2,1,15,5,0,20,10,0,10,15,1,3,1,0,1,2,1,0,3,5,2,4,7,6,7,4,
               2,2,1,2,2,2,2,6,1,8,6,5,2,5,4,2,5,2,3,3,1,2,1,1,3,2,3,15,2,2,1,4,
               1,2,1,1,1,2,1,2,1,1,2,2,1,2,1,1,1,1,1,2,10,2,5,10,20,10,5,10,10,5,
               20,15,10,5,20,20,15,10,25,15,20,15,10,15,2,15,5,5,3,1,5,1,5,2,1,0,
               5,4,1,2,1,3,5,5,5,5,10,8,1,5,10,5,5,2,10,2,2,10,1,5,5,1,1,10,5,2,
               5,1,3,2,5,10,10,5,10,1,10,3,15,1,10,5,2,3,5,10,3,15,30,5,20,1,2,2,
               1,3,7,8,10,5,7,5,9,6,5,8,9,7,6,5,5,7,6,2,3,10,10,15,5,1,2,5,2,1,3,
               10,1,5,1,10,1,5,1,2,15,5,1,15,1,5,5,10,15,5,2,10,0,0,5,6,0,1,2,0,3,
               0,1,5,7,2,5,1,2,1,10,2,2,2,5,5,10,5,0,5,2,10,1,1,3,10,3,1,4,2,0,1,
               5,1,8,5,5,1,3,5,5,2,1,5,5,5,5,0,5,0,13,10,2,9,2,0,0,5,5,5,5,5,0,1,
               0,2,1,5,4,2,5,4,1,1,5,1,1,15,10,5,0,15,15,0,0,4,5,2,15,5,15,3,3,
               10,10,5,3,7,13,0,0,2,4,1,2,4,1,5,3,8,10,10,5,10,2,5,10,7,10,8,2,5,
               7,6,7,5,2,5,1,2,1,8,4,10,5,15,10,5,3,1,5,2,5,1,2,5,1,1,5,2,1,5,0,
               10,20,5,5,2,2,10,5,2,0,1,1,2,1,1,1,1,1,1,1,1,2,1,3,1,1,5,2,3,1,2,
               0,1,1,5,1,5,2,2,2,5,5,5,15,15,5,10,5,5,15,5,10,5,10,5,7,5,1,5,7,5,
               10,1,2,3,2,1,2,1,3,5,3,5,3,2,4,5,2,1,5,5,20,5,10,10,10,10,5,3,5,2,
               10,4,1,3,5,5,4,7,5,3,5,2,2,10,4,0,8,2,4,3,15,5,2,8,3,10,5,20,2,0,
               0,10,1,1,1,1,1,1,0,0,2,0,10,20,2,10,2,1,3,2,2,5,3,4,1,5,3,1,1,7,2,
               4,5,4,5,5,5,10,1,1,3,5,5,0,0,1,1,1,5,0,0,0,0,1,1,2,0,3,0,10,1,2,1,
               1,10,0,2,2,5,1,5,3,5,1,3,3,10,0,0,0,5,5,1,2,1,1,2,3,10,10,5,4,1,5,
               5,2,3,1,1,5,1,2,25,0,5,5,2,3,1,1,2,1,2,1,5,5,5,5,15,5,5,1,3,2,5,2,
               4,2,10,1,7,10,20,5,10,5,1,3,10,2,20,10,15,1,10,1,5,1,3,2,5,6,3,10,
               3,15,7,5,10,1,1,1,1,1,1,4,1,10,0,0,0,0,0,2,0,0,2,0,0,0,10,5,2,2,3,
               3,4,1,2,2,10,8,1,3,1,4,15,5,1,5,0,2,0,3,2,3,0,1,5,2,1,0,1,3,1,10,0,
               3,3,1,1,1,5,1,1,1,1,1,1,3,1,3,2,10,0,10,2,10,1,1,1,1,1,1,1,0,3,0,1,
               3,0,1,4,3,5,1,10,5,2,5,10,2,2,3,15,10,10,5,10,5,2,5,5,10,2,1,2,0,5,
               5,2,2,2,2,2,10,10,10,3,10,2,1,1,2,3,1,5,2,1,1,3,4,1,2,1,3,2,1,1,2,
               1,2,0,1,3,5,1,3,3,2,1,2,3,2,5,3,2,3,1,3,8,1,4,2,2,4,5,11,1,6,2,10,
               3,0,0,0,20,10,15,5,15,7,7,10,3,5,2,3,1,0,0,0,0,5,1,3,2,1,1,1,2,1,2,
               2,5,2,1,1,2,1,2,0,0,3,0,0,0,2,2,5,5,5,1,60,15,2,0,3,5,5,1,2,10,2,0,
               2,15,5,1,20,3,0,10,0,5,10,0,0,10,0,0,5,0,5,2,2,10,1,1,5,1,5,2,5,2,
               15,20,15,5,5,5,15,5,2,10,20,1,1,2,1,1,5,1,5,3,3,1,3,15,6,15,10,10,
               15,20,10,1,1,1,3,3,4,4,15,1,10,5,5,4,0,1,2,2,2,2,3,2,3,5,2,1,1,2,
               3,2,5,15,4,3,1,5,0,1,2,1,3,0,1,5,1,1,0,5,0,0,0,10,5,5,5,5,10,0,1,
               1,2,15,10,30,1,1,0,2,3,2,4,5,10,3,10,1,1,1,7,3,1,3,3,3,10,5,3,2,7,
               0,5,2,0,30,20,10,10,10,10,10,10,10,10,10,5,5,5,5,10,2,5,5,2,20,5,
               30,15,10,5,6,5,20,1,10,10,1,1,5,5,1,5,5,10,15,15,5,10,10,5,3,3,5,
               10,5,0,5,5,1,5,5,15,20,5,5,5,1,15,5,20,1,2,10,1,2,0,1,5,5,10,1,5,
               1,1,1,1,1,2,2,10,10,3,5,0,3,1,1,1,0,1,3,1,1,5,0,10,5,0,0,3,3,5,0,
               0,1,10,5,5,3,10,10,10,2,35,20,25,15,5,5,2,2,5,2,5,0,3,3,1,30,10,
               15,5,20,5,10,10,20,15,5,10,5,5,15,20,15,5,0,1,4,10,3,4,26,5,10,10,
               1,5,0,0,5,5,5,5,10,30,2,2,5,1,3,3,1,1,1,3,1,3,7,3,15,20,0,15,5,25,
               3,25,0,30,0,5,1,1,2,1,1,5,10,5,0,0,20,1,0,15,5,5,15,15,15,15,15,10,
               10,15,10,30,30,20,20,5,5,1,4,4,5,5,10,2,0,5,1,1,15,15,5,4,1,1,3,3,
               1,0,15,0,10,20,15,5,4,0,0,2,1,0,2,0,2,1,1,2,2,1,0,5,4,3,3,5,5,2,1,
               5,4,2,10,2,2,10,3,3,5,10,1,0,10,5,0,10,5,10,5,10,10,60,30,30,99,0,
               2,1,0,1,1,2,1,2,1,5,1,1,1,5,5,5,1,0,1,0,0,0,0,3,3,10,2,5,2,2,1,5,3,
               6,2,3,7,5,3,1,1,1,1,1,5,5,5,5,7,2,5,5,10,2,2,5,5,5,10,5,5,5,5,5,5,
               10,15,5,5,5,5,0,2,10,0,2,5,0,1,10,2,1,1,2,4,5,1,2,2,0,5,2,2,3,3,1,
               1,10,0,3,0,1,10,12,3,2,6,9,3,5,2,1,1,1,3,4,5,10,5,10,15,20,6,5,5,
               5,1,5,15,5,5,10,8,3,15,12,0,5,2,5,5,3,5,4,1,1,3,1,5,2,10,20,1,15,
               15,10,3,1,3,2,0,5,0,1,0,1,2,2,1,1,0,1,10,1,5,1,1,1,4,0,5,1,1,15,10,
               1,5,5,5,1,10,0,10,2,1,99,99,99,99,99,5,1,10,30,3,5,5,10,10,0,10,0,
               4,1,12,5,1,4,1,3,0,15,3,10,5,1,2,1,1,1,2,1,0,1,1,3,5,2,25,15,20,1,
               5,2,10,3,3,4,1,3,2,1,5,3,10,1,10,5,1,25,5,20,10,20,15,15,10,10,18,
               0,5,1,0,5,2,10,5,5,2,5,5,3,1,3,2,0,2,1,5,99,99,99,99,99,99,99,99,
               99,99,2,5,1,3,5,5,0,2,5,7,10,2,15,3,30,20,2,1,0,1,0,1,2,5,4,1,1,1,
               2,2,0,2,2,2,2,2,1,3,10,20,15,10,2,3,5,10,5,0,10,10,10,15,1,1,9,2,
               1,7,5,5,5,3,2,2,1,2,1,1,5,1,20,2,5,15,5,5,3,5,2,3,15,1,5,3,5,0,5,5,
               10,5,7,1,1,1,3,20,1,3,0,5,1,1,1,15,30,5,35,15,5,5,5,2,2,1,1,15,1,
               4,3,2,3,1,5,3,1,3,3,2,10,1,5,1,5,1,2,7,30,20,15,5,30,10,10,5,10,10,
               10,5,5,0,5,10,10,10,10,10,5,15,10,15,15,15,10,15,20,15,20,20,5,5,
               20,10,10,5,1,0,2,5,2,5,5,1,2,2,2,10,1,2,7,2,15,15,15,5,15,5,10,1,
               20,2,1,99,0,2,0,5,2,5,1,10,5,5,5,1,5,2,2,5,5,5,3,5,1,0,5,15,7,2,4,
               5,5,10,2,10,10,10,3,3,10,5,5,15,5,10,10,2,5,20,5,5,1,5,10,15,1,3,
               2,1,3,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,2,2,1,1,1,1,1,3,3,1,5,7,10,
               2,5,10,15,2,5,2,2,3,4,3,2,5,4,10,5,3,2,2,2,5,1,1,5,2,5,5,10,5,15,
               1,1,1,1,15,2,5,2,10,3,5,2,1,6,5,1,5,5,1,3,5,3,1,4,5,3,5,4,1,8,5,1,
               5,5,9,5,5,9,4,3,4,2,5,2,1,5,10,10,5,1,10,1,5,1,1,3,2,1,5,3,3,5,1,
               5,1,2,2,0,7,7,2,0,1,3,10,1,2,1,1,5,5,1,5,1,1,2,0,5,15,5,15,5,5,15,
               2,2,1,1,10,1,5,10,1,1,1,1,15,1,4,1,1,1,2,1,10,1,5,15,5,10,15,3,1,
               1,1,0,5,5,5,0,5,7,1,7,9,2,1,6,5,10,2,2,5,2,8,1,1,1,1,2,5,10,1,10,
               1,7,5,4,5,5,5,10,10,15,5,0,10,15,99,99,99,99,5,1,1,2,5,1,5,1,5,5,
               10,10,5,10,5,5,10,2,15,0,1,0,7,5,0,1,0,0,5,5,5,3,10,5,3,1,10,15,3,
               6,6,1,3,2,0,15,2,20,10,0,1,0,2,5,15,5,2,1,1,5,5,1,5,1,20,15,15,1,
               1,2,1,3,0,5,3,0,0,5,6,3,5,6,4,1,2,4,1,10,5,6,3,7,10,5,10,10,5,2,5,
               1,1,5,1,2,5,2,5,2,2,2,5,1,8,1,1,1,1,1,4,7,0,3,3,1,3,2,1,6,1,0,2,1,
               0,5,1,1,6,1,5,1,3,3,3,3,7,2,10,4,3,5,5,7,3,5,3,6,1,5,1,4,4,3,2,1,
               1,2,1,2,15,18,5,0,1,5,0,3,5,0,0,0,1,1,1,3,0,0,1,2,0,2,20,2,4,2,2,
               34,0,1,0,4,10,0,7)

thesisdata <- data.table(id = seq(1:length(parktimes)), 
                         parktime = parktimes)

Anscombe <- function(x) {
  
  # https://github.com/broxtronix/pymultiscale/blob/master/pymultiscale/anscombe.py
  
  # Compute the Anscombe variance stabilizing transform.
  
  # the input x is noisy Poisson-distributed data 
  # the output fx has variance approximately equal to 1.
  
  # Reference: Anscombe, F. J. (1948), "The transformation of Poisson,
  # binomial and negative-binomial data", Biometrika 35 (3-4): 246-254
  
  return (2.0 * sqrt(x + 3.0 / 8.0))
}


CalculatePoissonDist <- function(thesisdata, colnam) {
  
  # According to:
  # https://www.sqlservercentral.com/articles/scoring-outliers-in-non-normal-data-with-r
  
  # We're going to use the ppois() function to calculate an "outlier score" for 
  # every observation in our dataset. The intuitive way to think about this 
  # score is the "likelihood of observing a point this large". This is a 
  # somewhat loose interpretation of a p-value, but suitable for detecting 
  # outliers.
  # This function fails if input dataframe is not a data.table dataframe.
  
  
  # Calculate Poisson distribution for parktime or walktime. Creates two new
  # columns, Score (double) and Outlier (boolean). Explicitly prints results
  # and returns the inputted dataframe with updates.
  
  # Try Anscombe transform for the parameter column
  anscombe_col <- paste0("anscombe_", colnam)
  thesisdata[, (anscombe_col) := Anscombe(thesisdata[, get(colnam)])]
  
  # Calculate a "p-value" for outliers, based on the poisson probabilities.
  # Use get() to enable string column names in data.table syntax
  thesisdata[, Score := 1 - ppois(q = get(anscombe_col), 
                                  lambda = mean(get(anscombe_col)))]
  
  # Apply a Bonferroni correction factor to the p-value, to control the long-run 
  # error rate
  thesisdata[, Outlier := Score < 0.05 / 1000]
  
  # Add a Method column with all values "Poisson"
  thesisdata[, Method := "Poisson"]
  
  # Visualise the results
  p <- ggplot(thesisdata, aes(x = id, y = !!sym(colnam))) + 
    geom_point(aes(colour = Outlier), size = 3, alpha = 0.7) +
    scale_colour_manual(values = c("darkgrey", "red")) +
    scale_y_continuous(breaks = scales::pretty_breaks(n = 10)) +
    theme_minimal()
  print(p)
  
  return(thesisdata) 
}

# Outliers in count data?
thesisdata <- CalculatePoissonDist(thesisdata, "parktime")
```

With Anscombe transform (y axis is parktime):

Without Anscombe transform:

My code:

library(ggplot2)
library(data.table)
library(outliers)

parktimes <- c(99,5,0,1,10,99,99,1,1,3,1,1,2,5,2,2,2,5,10,5,2,2,0,1,1,1,5,3,5,5,
               1,0,0,5,1,0,0,2,2,0,5,10,1,1,1,5,5,3,10,1,1,1,1,0,10,2,10,7,10,7,
               3,3,13,1,3,1,1,1,4,4,1,2,3,1,1,1,1,1,1,2,1,1,2,3,0,7,8,3,3,3,5,4,
               25,0,10,0,10,6,3,0,0,1,2,1,0,0,0,0,0,0,3,1,0,1,2,1,0,1,5,5,5,3,0,
               0,0,0,2,1,3,0,1,5,5,5,2,0,2,0,5,15,3,4,3,4,2,5,1,10,10,2,0,1,1,1,
               0,0,1,0,10,5,15,1,10,0,0,2,1,5,1,1,2,2,3,1,1,1,1,4,4,1,3,3,1,3,1,
               2,1,0,1,2,2,5,1,2,1,3,5,1,1,1,1,5,4,5,2,15,15,2,5,2,5,8,2,8,5,5,2,
               0,1,3,2,1,1,1,1,1,1,1,1,10,3,1,8,10,10,12,5,5,3,6,4,2,1,3,2,0,0,1,
               3,1,1,1,1,2,1,3,1,1,2,1,1,3,1,1,1,3,2,1,1,2,2,1,4,1,1,1,1,2,1,2,3,
               4,1,2,1,2,10,1,0,0,3,3,10,1,4,0,2,5,5,1,4,0,5,1,1,1,3,0,1,5,1,1,1,
               1,1,1,5,5,5,5,5,10,20,1,1,1,0,0,0,0,1,0,2,0,2,2,2,0,1,1,1,2,2,2,0,
               1,0,1,2,1,5,0,0,10,1,2,1,2,2,3,2,3,1,1,2,5,2,1,5,5,2,10,2,4,0,5,0,
               1,1,5,1,2,5,1,1,3,4,1,6,6,5,2,10,10,10,60,7,1,15,10,0,5,15,1,0,2,
               0,0,0,2,1,2,3,3,2,2,3,3,2,3,1,3,5,1,2,1,3,10,1,1,1,1,5,3,1,6,12,5,
               7,6,5,2,0,3,1,5,10,30,45,45,30,45,0,0,0,0,5,5,0,3,5,2,5,10,10,2,5,
               10,2,1,30,5,2,2,7,1,1,2,4,5,5,1,1,1,5,2,2,2,2,1,5,0,1,3,5,5,1,2,
               15,10,0,1,10,8,10,25,5,10,5,12,20,7,12,2,5,2,10,3,10,5,5,5,5,5,7,
               3,7,3,6,9,7,1,1,10,10,1,1,1,1,2,1,15,30,1,10,5,20,1,10,1,35,10,0,
               5,25,35,10,1,5,5,10,20,5,5,5,10,10,15,2,2,1,1,1,1,1,3,5,5,5,1,1,5,
               10,10,15,15,25,20,5,15,5,0,5,5,2,5,3,10,2,5,5,1,15,8,4,6,5,15,20,
               20,20,15,15,15,30,15,10,5,5,10,10,10,10,5,5,0,10,1,5,1,2,0,2,2,5,
               10,15,3,15,3,4,3,2,1,3,4,5,4,2,10,1,1,1,1,5,1,10,5,5,10,5,1,5,7,
               10,10,5,10,5,1,2,15,10,1,10,10,15,10,10,5,2,2,2,5,5,10,5,5,2,5,5,
               2,5,10,10,20,5,1,2,2,5,2,5,1,1,15,10,20,15,4,15,15,5,15,5,0,5,1,0,
               0,5,6,7,1,3,2,3,2,0,10,15,10,10,3,30,10,30,5,10,20,10,0,1,10,1,2,
               2,1,1,0,1,10,0,10,15,5,5,10,5,8,4,10,10,3,3,5,5,1,4,0,15,2,10,10,
               2,2,10,2,5,10,1,1,1,1,1,2,2,1,1,1,2,1,1,2,2,8,4,5,1,3,5,10,1,2,1,
               2,1,0,1,0,8,10,3,15,0,0,0,1,2,0,1,0,5,2,10,5,2,10,5,1,1,0,2,5,1,1,
               1,3,2,3,2,2,6,9,9,9,8,2,9,10,5,10,1,15,10,4,5,5,5,1,7,1,10,2,2,8,
               2,2,7,1,1,10,2,8,10,2,5,5,4,3,5,5,8,6,8,4,2,10,15,4,8,3,6,5,5,6,0,
               1,10,15,10,3,5,1,8,10,7,1,1,2,5,10,10,15,0,2,5,5,5,10,3,5,1,4,1,1,
               14,24,5,5,15,3,0,5,0,5,5,6,0,1,2,1,1,4,1,10,2,5,1,1,5,8,5,10,19,0,
               3,5,2,5,0,2,2,5,1,2,2,5,1,2,2,1,5,2,2,1,1,5,15,1,1,1,5,1,1,7,5,3,
               5,1,10,1,1,2,4,1,1,2,4,2,1,0,1,2,1,10,5,10,3,15,1,1,15,5,10,1,1,
               1,10,20,20,5,1,10,15,1,10,5,1,5,5,5,5,5,20,20,5,1,5,5,10,5,5,20,
               5,15,15,10,2,0,0,3,2,5,1,2,1,0,3,0,5,1,1,1,5,1,1,5,10,10,0,1,1,1,
               1,5,5,10,5,5,1,8,10,10,10,2,3,5,3,15,3,5,0,0,0,1,1,1,1,0,1,1,1,1,
               1,1,1,1,0,1,2,1,1,1,1,0,1,1,1,10,15,10,10,10,20,5,3,1,7,7,5,20,1,
               2,5,5,5,5,0,7,1,5,1,1,1,1,1,1,5,1,3,1,3,2,2,5,0,45,5,10,10,5,10,5,
               1,2,5,2,5,2,1,1,5,2,15,20,10,35,5,5,5,5,10,20,15,15,1,2,5,5,2,2,3,
               5,1,1,10,10,1,1,1,0,2,3,7,2,1,2,2,1,2,3,4,2,1,28,20,1,5,5,8,2,0,0,
               3,8,1,3,2,15,15,15,8,4,20,0,2,2,5,1,1,5,7,5,0,5,1,15,2,2,12,10,6,
               15,0,2,4,5,5,10,1,1,1,1,2,6,2,1,0,1,3,3,5,3,6,8,2,60,90,15,3,10,1,
               5,3,1,6,1,2,2,7,3,3,15,25,10,5,10,8,7,1,1,1,5,3,5,1,2,5,0,1,2,1,2,
               1,1,1,1,5,2,25,20,0,0,4,1,5,1,15,10,1,1,3,1,1,5,6,5,1,14,15,6,15,
               8,7,1,4,8,5,2,1,0,1,1,1,2,6,3,5,5,2,8,4,1,10,5,4,8,3,3,3,1,3,2,1,
               2,3,1,2,6,3,4,6,2,8,1,5,5,1,2,6,1,3,1,2,0,1,5,3,1,3,5,3,5,7,2,5,
               15,2,2,5,1,3,5,7,10,5,5,10,10,10,5,2,10,7,20,2,5,10,5,2,2,4,3,5,
               2,1,10,2,5,20,5,20,5,1,0,0,2,2,1,5,30,99,10,1,5,10,10,5,2,10,1,5,
               3,2,10,4,1,5,5,2,10,5,1,2,10,4,5,3,2,2,1,0,2,55,0,3,10,3,20,5,20,
               5,5,3,5,5,5,3,1,5,10,10,5,1,10,0,2,5,1,2,20,5,2,10,5,5,8,1,5,10,2,
               5,1,3,1,2,3,5,1,1,5,5,20,5,5,15,1,5,1,5,1,5,99,99,20,99,99,99,99,
               2,2,2,1,2,3,1,2,2,1,2,1,2,1,1,2,2,2,1,2,1,1,1,1,1,1,1,1,4,1,1,1,
               2,2,3,2,3,2,1,2,3,2,2,2,2,5,2,5,5,3,2,3,2,3,3,5,2,5,5,1,1,1,1,3,2,
               2,3,3,2,10,5,1,3,3,0,2,10,5,2,2,3,2,5,3,2,15,5,7,10,1,5,5,2,2,3,2,
               2,10,10,15,2,5,15,5,10,6,3,5,2,5,5,5,8,4,4,5,5,4,2,2,5,2,5,5,0,5,
               2,5,5,0,0,0,5,10,5,10,1,5,5,1,1,3,20,20,0,0,3,0,2,1,2,1,1,2,1,1,8,
               2,2,5,5,0,3,20,6,1,2,4,1,15,2,4,5,5,2,5,10,5,1,1,1,3,2,1,2,3,4,6,
               5,10,5,5,2,10,10,10,10,10,10,0,10,10,5,10,10,5,5,5,10,10,10,5,1,1,
               3,10,5,5,1,1,0,0,2,10,10,5,5,5,2,2,5,2,10,5,10,1,10,3,2,1,3,2,3,3,
               5,1,1,2,6,3,5,5,10,5,3,5,5,10,5,4,5,3,3,1,2,1,3,5,1,1,1,1,1,2,2,5,
               6,2,4,2,2,2,5,10,2,2,3,3,2,1,2,2,4,2,1,5,10,5,1,1,3,0,5,3,5,5,1,2,
               2,5,3,1,10,2,5,3,10,10,3,10,5,2,3,10,0,2,3,2,1,0,10,2,0,1,2,4,2,2,
               5,2,7,0,0,5,7,7,5,1,5,10,5,1,3,4,6,5,2,15,5,4,10,3,2,10,3,3,4,10,
               2,8,5,0,2,1,1,3,3,1,1,1,1,1,1,2,1,3,1,1,10,2,1,1,0,1,0,10,30,5,15,
               5,5,10,5,5,5,5,1,0,0,0,7,1,5,5,2,1,2,5,20,30,15,15,1,0,0,0,0,2,5,
               0,0,0,3,0,0,2,5,0,0,4,0,1,2,3,0,4,3,1,1,3,20,5,5,10,10,15,15,10,5,
               3,1,4,10,10,2,10,2,1,5,5,2,2,2,1,1,1,1,1,3,2,2,3,1,7,1,1,3,1,1,3,
               3,2,5,2,2,5,5,2,1,3,1,1,1,2,5,5,1,10,2,3,5,1,5,10,0,5,5,0,0,3,3,1,
               1,1,15,3,15,2,2,5,1,5,0,1,1,2,2,1,4,5,1,3,2,10,3,5,7,10,3,3,3,4,3,
               2,2,0,0,1,1,4,1,3,1,1,3,5,1,10,15,3,3,1,1,5,5,2,10,2,5,5,7,5,8,7,
               6,4,5,4,4,2,8,10,9,15,8,5,0,0,2,5,0,5,1,3,2,5,20,10,30,10,30,15,
               10,15,15,10,10,10,10,5,15,1,1,2,0,1,4,5,5,0,2,5,4,1,2,0,0,1,2,1,5,
               6,1,1,3,1,1,1,1,3,5,10,5,5,2,5,0,1,3,0,3,5,5,15,10,10,0,5,10,5,2,
               10,5,2,10,5,2,5,10,5,1,20,5,15,5,5,5,5,5,5,5,10,10,5,5,5,5,5,10,5,
               0,0,10,10,5,5,1,25,5,1,1,5,1,2,1,1,1,2,3,10,1,30,10,20,10,20,5,15,
               10,10,15,25,15,1,0,7,2,1,0,3,3,4,15,5,15,10,3,10,5,3,2,1,1,3,1,3,
               25,0,10,5,7,5,20,10,18,20,5,2,1,1,1,1,1,1,2,2,5,2,2,5,5,10,5,10,10,
               3,2,1,1,8,5,2,2,5,5,5,1,5,5,2,15,0,0,2,10,5,1,1,2,0,5,1,5,5,5,2,10,
               5,0,5,5,1,4,1,0,4,0,3,4,1,1,0,0,3,5,1,2,1,10,5,5,2,2,3,0,20,2,5,1,0,
               3,1,5,5,15,5,5,5,2,0,3,3,0,0,5,5,5,1,2,3,1,10,10,1,1,3,1,0,5,0,10,5,
               10,10,10,0,2,3,2,0,10,2,15,2,6,2,10,5,2,3,10,3,5,3,3,5,3,5,4,3,10,5,
               5,5,10,2,4,5,6,8,5,5,4,2,15,4,15,5,10,5,5,2,1,1,1,2,3,2,3,4,5,0,10,
               15,5,5,1,3,15,1,10,3,1,10,5,5,5,3,7,8,1,10,3,3,0,0,7,15,15,5,3,15,
               2,10,1,7,5,20,2,10,5,1,1,1,2,1,5,15,15,5,1,5,7,9,3,2,5,5,15,10,20,
               0,20,25,5,15,10,2,3,2,2,5,2,1,5,5,6,6,1,1,3,1,1,3,3,10,2,20,20,5,5,
               4,0,30,20,5,15,0,10,10,1,6,3,1,2,2,10,2,1,1,1,0,10,2,2,5,5,4,5,16,
               2,1,10,30,15,5,3,2,10,10,1,3,1,3,2,2,10,2,1,3,1,1,1,1,3,3,5,7,5,3,
               10,5,1,10,2,2,1,1,5,1,2,3,2,2,2,5,1,1,1,10,2,1,1,1,3,1,6,1,3,5,1,
               3,10,10,0,0,0,0,0,15,10,10,15,1,7,3,5,5,1,5,10,6,2,4,2,2,1,1,4,2,
               1,2,4,1,3,3,1,1,1,2,1,2,2,2,4,1,1,1,2,2,1,2,1,2,4,4,2,1,8,3,1,3,2,
               5,5,2,2,4,3,3,1,1,1,2,1,2,2,1,2,3,2,2,5,0,0,0,3,5,1,1,1,1,2,2,5,5,
               5,0,4,1,1,5,10,5,5,3,1,3,3,4,5,1,3,2,3,3,3,2,3,2,4,5,3,5,2,5,5,6,1,
               3,7,4,30,3,1,1,3,15,10,2,1,5,1,1,2,1,3,1,1,2,3,1,1,1,1,1,2,1,1,10,
               2,2,2,2,5,1,25,30,10,3,15,5,5,30,20,20,40,35,20,10,5,0,5,2,15,20,
               2,7,10,2,2,1,15,5,0,20,10,0,10,15,1,3,1,0,1,2,1,0,3,5,2,4,7,6,7,4,
               2,2,1,2,2,2,2,6,1,8,6,5,2,5,4,2,5,2,3,3,1,2,1,1,3,2,3,15,2,2,1,4,
               1,2,1,1,1,2,1,2,1,1,2,2,1,2,1,1,1,1,1,2,10,2,5,10,20,10,5,10,10,5,
               20,15,10,5,20,20,15,10,25,15,20,15,10,15,2,15,5,5,3,1,5,1,5,2,1,0,
               5,4,1,2,1,3,5,5,5,5,10,8,1,5,10,5,5,2,10,2,2,10,1,5,5,1,1,10,5,2,
               5,1,3,2,5,10,10,5,10,1,10,3,15,1,10,5,2,3,5,10,3,15,30,5,20,1,2,2,
               1,3,7,8,10,5,7,5,9,6,5,8,9,7,6,5,5,7,6,2,3,10,10,15,5,1,2,5,2,1,3,
               10,1,5,1,10,1,5,1,2,15,5,1,15,1,5,5,10,15,5,2,10,0,0,5,6,0,1,2,0,3,
               0,1,5,7,2,5,1,2,1,10,2,2,2,5,5,10,5,0,5,2,10,1,1,3,10,3,1,4,2,0,1,
               5,1,8,5,5,1,3,5,5,2,1,5,5,5,5,0,5,0,13,10,2,9,2,0,0,5,5,5,5,5,0,1,
               0,2,1,5,4,2,5,4,1,1,5,1,1,15,10,5,0,15,15,0,0,4,5,2,15,5,15,3,3,
               10,10,5,3,7,13,0,0,2,4,1,2,4,1,5,3,8,10,10,5,10,2,5,10,7,10,8,2,5,
               7,6,7,5,2,5,1,2,1,8,4,10,5,15,10,5,3,1,5,2,5,1,2,5,1,1,5,2,1,5,0,
               10,20,5,5,2,2,10,5,2,0,1,1,2,1,1,1,1,1,1,1,1,2,1,3,1,1,5,2,3,1,2,
               0,1,1,5,1,5,2,2,2,5,5,5,15,15,5,10,5,5,15,5,10,5,10,5,7,5,1,5,7,5,
               10,1,2,3,2,1,2,1,3,5,3,5,3,2,4,5,2,1,5,5,20,5,10,10,10,10,5,3,5,2,
               10,4,1,3,5,5,4,7,5,3,5,2,2,10,4,0,8,2,4,3,15,5,2,8,3,10,5,20,2,0,
               0,10,1,1,1,1,1,1,0,0,2,0,10,20,2,10,2,1,3,2,2,5,3,4,1,5,3,1,1,7,2,
               4,5,4,5,5,5,10,1,1,3,5,5,0,0,1,1,1,5,0,0,0,0,1,1,2,0,3,0,10,1,2,1,
               1,10,0,2,2,5,1,5,3,5,1,3,3,10,0,0,0,5,5,1,2,1,1,2,3,10,10,5,4,1,5,
               5,2,3,1,1,5,1,2,25,0,5,5,2,3,1,1,2,1,2,1,5,5,5,5,15,5,5,1,3,2,5,2,
               4,2,10,1,7,10,20,5,10,5,1,3,10,2,20,10,15,1,10,1,5,1,3,2,5,6,3,10,
               3,15,7,5,10,1,1,1,1,1,1,4,1,10,0,0,0,0,0,2,0,0,2,0,0,0,10,5,2,2,3,
               3,4,1,2,2,10,8,1,3,1,4,15,5,1,5,0,2,0,3,2,3,0,1,5,2,1,0,1,3,1,10,0,
               3,3,1,1,1,5,1,1,1,1,1,1,3,1,3,2,10,0,10,2,10,1,1,1,1,1,1,1,0,3,0,1,
               3,0,1,4,3,5,1,10,5,2,5,10,2,2,3,15,10,10,5,10,5,2,5,5,10,2,1,2,0,5,
               5,2,2,2,2,2,10,10,10,3,10,2,1,1,2,3,1,5,2,1,1,3,4,1,2,1,3,2,1,1,2,
               1,2,0,1,3,5,1,3,3,2,1,2,3,2,5,3,2,3,1,3,8,1,4,2,2,4,5,11,1,6,2,10,
               3,0,0,0,20,10,15,5,15,7,7,10,3,5,2,3,1,0,0,0,0,5,1,3,2,1,1,1,2,1,2,
               2,5,2,1,1,2,1,2,0,0,3,0,0,0,2,2,5,5,5,1,60,15,2,0,3,5,5,1,2,10,2,0,
               2,15,5,1,20,3,0,10,0,5,10,0,0,10,0,0,5,0,5,2,2,10,1,1,5,1,5,2,5,2,
               15,20,15,5,5,5,15,5,2,10,20,1,1,2,1,1,5,1,5,3,3,1,3,15,6,15,10,10,
               15,20,10,1,1,1,3,3,4,4,15,1,10,5,5,4,0,1,2,2,2,2,3,2,3,5,2,1,1,2,
               3,2,5,15,4,3,1,5,0,1,2,1,3,0,1,5,1,1,0,5,0,0,0,10,5,5,5,5,10,0,1,
               1,2,15,10,30,1,1,0,2,3,2,4,5,10,3,10,1,1,1,7,3,1,3,3,3,10,5,3,2,7,
               0,5,2,0,30,20,10,10,10,10,10,10,10,10,10,5,5,5,5,10,2,5,5,2,20,5,
               30,15,10,5,6,5,20,1,10,10,1,1,5,5,1,5,5,10,15,15,5,10,10,5,3,3,5,
               10,5,0,5,5,1,5,5,15,20,5,5,5,1,15,5,20,1,2,10,1,2,0,1,5,5,10,1,5,
               1,1,1,1,1,2,2,10,10,3,5,0,3,1,1,1,0,1,3,1,1,5,0,10,5,0,0,3,3,5,0,
               0,1,10,5,5,3,10,10,10,2,35,20,25,15,5,5,2,2,5,2,5,0,3,3,1,30,10,
               15,5,20,5,10,10,20,15,5,10,5,5,15,20,15,5,0,1,4,10,3,4,26,5,10,10,
               1,5,0,0,5,5,5,5,10,30,2,2,5,1,3,3,1,1,1,3,1,3,7,3,15,20,0,15,5,25,
               3,25,0,30,0,5,1,1,2,1,1,5,10,5,0,0,20,1,0,15,5,5,15,15,15,15,15,10,
               10,15,10,30,30,20,20,5,5,1,4,4,5,5,10,2,0,5,1,1,15,15,5,4,1,1,3,3,
               1,0,15,0,10,20,15,5,4,0,0,2,1,0,2,0,2,1,1,2,2,1,0,5,4,3,3,5,5,2,1,
               5,4,2,10,2,2,10,3,3,5,10,1,0,10,5,0,10,5,10,5,10,10,60,30,30,99,0,
               2,1,0,1,1,2,1,2,1,5,1,1,1,5,5,5,1,0,1,0,0,0,0,3,3,10,2,5,2,2,1,5,3,
               6,2,3,7,5,3,1,1,1,1,1,5,5,5,5,7,2,5,5,10,2,2,5,5,5,10,5,5,5,5,5,5,
               10,15,5,5,5,5,0,2,10,0,2,5,0,1,10,2,1,1,2,4,5,1,2,2,0,5,2,2,3,3,1,
               1,10,0,3,0,1,10,12,3,2,6,9,3,5,2,1,1,1,3,4,5,10,5,10,15,20,6,5,5,
               5,1,5,15,5,5,10,8,3,15,12,0,5,2,5,5,3,5,4,1,1,3,1,5,2,10,20,1,15,
               15,10,3,1,3,2,0,5,0,1,0,1,2,2,1,1,0,1,10,1,5,1,1,1,4,0,5,1,1,15,10,
               1,5,5,5,1,10,0,10,2,1,99,99,99,99,99,5,1,10,30,3,5,5,10,10,0,10,0,
               4,1,12,5,1,4,1,3,0,15,3,10,5,1,2,1,1,1,2,1,0,1,1,3,5,2,25,15,20,1,
               5,2,10,3,3,4,1,3,2,1,5,3,10,1,10,5,1,25,5,20,10,20,15,15,10,10,18,
               0,5,1,0,5,2,10,5,5,2,5,5,3,1,3,2,0,2,1,5,99,99,99,99,99,99,99,99,
               99,99,2,5,1,3,5,5,0,2,5,7,10,2,15,3,30,20,2,1,0,1,0,1,2,5,4,1,1,1,
               2,2,0,2,2,2,2,2,1,3,10,20,15,10,2,3,5,10,5,0,10,10,10,15,1,1,9,2,
               1,7,5,5,5,3,2,2,1,2,1,1,5,1,20,2,5,15,5,5,3,5,2,3,15,1,5,3,5,0,5,5,
               10,5,7,1,1,1,3,20,1,3,0,5,1,1,1,15,30,5,35,15,5,5,5,2,2,1,1,15,1,
               4,3,2,3,1,5,3,1,3,3,2,10,1,5,1,5,1,2,7,30,20,15,5,30,10,10,5,10,10,
               10,5,5,0,5,10,10,10,10,10,5,15,10,15,15,15,10,15,20,15,20,20,5,5,
               20,10,10,5,1,0,2,5,2,5,5,1,2,2,2,10,1,2,7,2,15,15,15,5,15,5,10,1,
               20,2,1,99,0,2,0,5,2,5,1,10,5,5,5,1,5,2,2,5,5,5,3,5,1,0,5,15,7,2,4,
               5,5,10,2,10,10,10,3,3,10,5,5,15,5,10,10,2,5,20,5,5,1,5,10,15,1,3,
               2,1,3,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,2,2,1,1,1,1,1,3,3,1,5,7,10,
               2,5,10,15,2,5,2,2,3,4,3,2,5,4,10,5,3,2,2,2,5,1,1,5,2,5,5,10,5,15,
               1,1,1,1,15,2,5,2,10,3,5,2,1,6,5,1,5,5,1,3,5,3,1,4,5,3,5,4,1,8,5,1,
               5,5,9,5,5,9,4,3,4,2,5,2,1,5,10,10,5,1,10,1,5,1,1,3,2,1,5,3,3,5,1,
               5,1,2,2,0,7,7,2,0,1,3,10,1,2,1,1,5,5,1,5,1,1,2,0,5,15,5,15,5,5,15,
               2,2,1,1,10,1,5,10,1,1,1,1,15,1,4,1,1,1,2,1,10,1,5,15,5,10,15,3,1,
               1,1,0,5,5,5,0,5,7,1,7,9,2,1,6,5,10,2,2,5,2,8,1,1,1,1,2,5,10,1,10,
               1,7,5,4,5,5,5,10,10,15,5,0,10,15,99,99,99,99,5,1,1,2,5,1,5,1,5,5,
               10,10,5,10,5,5,10,2,15,0,1,0,7,5,0,1,0,0,5,5,5,3,10,5,3,1,10,15,3,
               6,6,1,3,2,0,15,2,20,10,0,1,0,2,5,15,5,2,1,1,5,5,1,5,1,20,15,15,1,
               1,2,1,3,0,5,3,0,0,5,6,3,5,6,4,1,2,4,1,10,5,6,3,7,10,5,10,10,5,2,5,
               1,1,5,1,2,5,2,5,2,2,2,5,1,8,1,1,1,1,1,4,7,0,3,3,1,3,2,1,6,1,0,2,1,
               0,5,1,1,6,1,5,1,3,3,3,3,7,2,10,4,3,5,5,7,3,5,3,6,1,5,1,4,4,3,2,1,
               1,2,1,2,15,18,5,0,1,5,0,3,5,0,0,0,1,1,1,3,0,0,1,2,0,2,20,2,4,2,2,
               34,0,1,0,4,10,0,7)

thesisdata <- data.table(id = seq(1:length(parktimes)), 
                         parktime = parktimes)

Anscombe <- function(x) {
  
  # https://github.com/broxtronix/pymultiscale/blob/master/pymultiscale/anscombe.py
  
  # Compute the Anscombe variance stabilizing transform.
  
  # the input x is noisy Poisson-distributed data 
  # the output fx has variance approximately equal to 1.
  
  # Reference: Anscombe, F. J. (1948), "The transformation of Poisson,
  # binomial and negative-binomial data", Biometrika 35 (3-4): 246-254
  
  return (2.0 * sqrt(x + 3.0 / 8.0))
}


CalculatePoissonDist <- function(thesisdata, colnam) {
  
  # According to:
  # https://www.sqlservercentral.com/articles/scoring-outliers-in-non-normal-data-with-r
  
  # We're going to use the ppois() function to calculate an "outlier score" for 
  # every observation in our dataset. The intuitive way to think about this 
  # score is the "likelihood of observing a point this large". This is a 
  # somewhat loose interpretation of a p-value, but suitable for detecting 
  # outliers.
  # This function fails if input dataframe is not a data.table dataframe.
  
  
  # Calculate Poisson distribution for parktime or walktime. Creates two new
  # columns, Score (double) and Outlier (boolean). Explicitly prints results
  # and returns the inputted dataframe with updates.
  
  # Try Anscombe transform for the parameter column
  anscombe_col <- paste0("anscombe_", colnam)
  thesisdata[, (anscombe_col) := Anscombe(thesisdata[, get(colnam)])]
  
  # Calculate a "p-value" for outliers, based on the poisson probabilities.
  # Use get() to enable string column names in data.table syntax
  thesisdata[, Score := 1 - ppois(q = get(anscombe_col), 
                                  lambda = mean(get(anscombe_col)))]
  
  # Apply a Bonferroni correction factor to the p-value, to control the long-run 
  # error rate
  thesisdata[, Outlier := Score < 0.05 / 1000]
  
  # Add a Method column with all values "Poisson"
  thesisdata[, Method := "Poisson"]
  
  # Visualise the results
  p <- ggplot(thesisdata, aes(x = id, y = !!sym(colnam))) + 
    geom_point(aes(colour = Outlier), size = 3, alpha = 0.7) +
    scale_colour_manual(values = c("darkgrey", "red")) +
    scale_y_continuous(breaks = scales::pretty_breaks(n = 10)) +
    theme_minimal()
  print(p)
  
  return(thesisdata) 
}

# Outliers in count data?
thesisdata <- CalculatePoissonDist(thesisdata, "parktime")