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## Abstract

We use US Social Security Administration data to compute the probability of a name clash in a class of year-YYYY born kids during the years 1880-2014.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. The markdown+Rknitr source code of this blog is available under a GNU General Public License (GPL v3) license from .

## Introduction

After reading a cool post by Kasia Kulma on how the release of Disney films have an impact on girl namings in the US, I became aware of the `babynames`

package by Hadley Wickham. The package wraps the data by the USA social security administration on the frequency of all baby names each year during the period 1880-2014 in the US. For reasons of privacy protection, only names with 5 or more occurrences in a given year, are contained in the data.

`library(babynames)`

Check how many unique names are contained in the data each year:

`babynames %>% group_by(year) %>% summarise(n=n()) %>% ggplot(aes(x=year, y=n)) + geom_line() + xlab("Time (years)") + ylab("Number of different names in the data")`

We look at the proportion of babies, which apparently have been removed due to privacy protection of the names. This is done by investigating the sum of proportions for each year. If all names would be available, the sum would be 2 (1 for each gender).

It becomes clear that a non-negligible part of the data appear to have been removed. Due to these names being removed, we re-scale the yearly proportions s.t. they really sum to one.

`babynames <- babynames %>% group_by(year) %>% mutate(p = n/sum(n))`

### Birthday Problem with Unequal Occurrence Probabilities

The data are perfect for testing the name-collision functionality from the previous Happy pbirthday class of 2016 post. Since the post, the `pbirthday_up`

function for computing the name collision probability for the birthday problem with unequal occurrence probabilities, has been assembled into a preliminary `birthdayproblem`

package.

We can now easily calculate for each year the probability that 2 or more kids in a class of \(n=26\) kids all born in a given year YYYY will have same first name:

It looks like the name distribution has become more diverse over time, since the collision probability reduces over time. However, some bias is to be expected due to the removal of names with frequencies below 5 in a given year.

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**Theory meets practice...**.

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