Naming Uncertainty: Ranks and Collisions

Pre-Print Version of the Article

• Naming Uncertainty: Ranks and Collisions

Data

• Baby Names Statistics by the Office for National Statistics (ONS), which contains the frequency of all names occurring more than 2 times in a given year.
  
• 2015 Data used for the article: Boys (2015) | Girls (2015)
• Additional information for the 2015 data provided by the ONS customer service:
• Boys:
  Number of names that occurred twice in 2015: 3,050
  Number of names that occurred once in 2015: 18,741
• Girls:
  Number of names that occurred twice in 2015:  3,999
  Number of names that occurred once in 2015: 23,733
• In 2016 the number of names occurring only once or twice per gender are now directly included as Table 1 of the ONS Bulletin
  
• Alternatively one can find the ONS data without the additional information in the R package ukbabynames.
  

Software and Computations

• Github project naming containing
  
• the R code of the ONS data pre-processing (automatic downloading, data loading and formatting)
• knitr::purl output of the Rmarkdown code generating the article. This includes code to generate all the numbers of the article
• HTML output of running the R part of the Rmarkdown code
  
• code for the creation of the bonus material below

• R-package birthdayproblem, which allows one to solve the birthday problem with unequal occurrence probabilities

Background 

• Original post containing a descriptive analysis of Berlin's open access baby names statistics data
  
• Blog post about the details for computing the birthday problem with unequal occurrence probabilities
• Blog post performing a time series analysis of the collision probability based on US name data 1880-2014
  
• Blog post performing a similar time series analysis for the collision probability for Swedish name data 1998-2016

Bonus Material

Instead of by tables the frequencies of the 2015 baby names can also be visualized using word clouds. The size of the name is proportional to the number of births in 2015.

Based on the ONS Baby Names Statistics data available for the years 1996-2016 containing all names in a given year occurring more than twice, we can compute the yearly collision probability. Note: The computed probability will be an upper limit to the actual collision probability, because no statistics is available for names occurring once or twice. However, for 2015 this information was obtained from the ONS (see above), upon request the ONS in 2016 incorporated this information directly into their bulletin. As a consequence, we can compute the correct collision probability for 2015-2016 as done in the article. The obtained time series plot can be compared to similar plots for the US 1880-2014 as well as Sweden 1998-2016.

Figure: Collision probability for the cohorts born 1996-2016 based on the baby names datasets containing all names with more than two uses in a given year. The orangish line in the figure indicates the collision probability for 2015-2016 computed on all names, i.e. also those including those names occurring just once or twice in a given year.