I am not a statistics expert but was interested in the validity of the reasoning below.

Somebody argued that many people had the letter 'J' in their initials. Can someone comment on the validity of the following approach and how it could be improved, notably what probability distribution would a list of firs tnames sorted by popularity follows?

According to wikipedia the most common first names for males in the US according to the 1990 census are, in that order:

'James','John','Robert','Michael','William','David','Richard','Charles','Joseph', and 'Thomas'

Let's use an approximate probability distribution (any better way?) that gives the probabilities to these names according to their order i (starting at 0) following:

P(name_i) = 0.15 / (i + 2)

This is a probability distribution for at least 1000 names (sums to 1), and starts like this:

0.0749, 0.0499, 0.0374, 0.0299, 0.0249, ...

meaning that someone has 7.49% chances of being called James. The sum of the probabilities of having a name starting with J from these list is 14% (P(James)+P(John)+P(Joseph)), lets call it Pj. Of course Pj is in fact higher because more names than these 8 in the list of 1000 may start with J.

Now let's assume a child is given three first names, the probability that at least of them starts with J given pj is 36%!! (from (1-(1-pj)^3)). So every time you meet a new person, you have one third chances to see him having a J on his business card. Let's call this probability pIj, probability of at least one initial starting with a J.

However, when you say overwhelming majority, let's assume that you mean 8 out of 10. The probability that out of 10 people you meet in a row 8 have a name starting with a J is, using binomial distribution, only 0.5% I'm afraid, by comb(10,8)pIj^8(1-pIj)^2 .

However, if you settle with 5 our of 10, your chances rise to 16%.

FYI the original question and post can be found here.

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    $\begingroup$ It seems to me that you systematically replace information that could be obtained from data by assumptions that have little or no objective support, including the assumed probability distribution, that you meet people at random, that names are assigned independently, that you can ignore the J's in the next 992 names, etc. This kind of exercise can be useful to get a sense of what a solution might look like and what assumptions are important to verify, but it's unrealistic to suppose that the actual chances you obtain can be trusted. $\endgroup$ – whuber Feb 13 '12 at 22:51
  • $\begingroup$ You're right, and I guess that the more experienced you are the more assumptions get realistic. The tradeoff is between getting a sense of what the solution might look like and doing the research, which is not justified when the question is of anecdotal interest only. Something akin to estimates and order-of-magnitude calculations in engineering. $\endgroup$ – Vladtn Feb 14 '12 at 14:35
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    $\begingroup$ Actual frequencies of male given names in the 1990 US census can be found at names.mongabay.com/male_names.htm $\endgroup$ – Pere Dec 11 '16 at 22:24

Surname frequencies, like the relative frequencies for many types of words, tend to follow a zeta distribution, possibly produced by an effect like Zipf's law (See here for more details)

So the sort of distribution you've suggested seems reasonable. Probably the empirical distribution differs quite a bit though, and fluctuates from year to year. If you're a young person, who mostly interacts with people ages 5-10, for example, then this could quite strongly affect the probability of meeting 8 out of 10 people with a J.

Further, I'm not certain that the distribution of given names matches that for surnames.

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