3 ms·

No, it depends on the distribution. Let's say (as a first guess) that number of children follow a poisson distribution. A poisson distribution with mean of 1.84

by tel 17y ago

No, it depends on the distribution. Let's say (as a first guess) that number of children follow a poisson distribution. A poisson distribution with mean of 1.84 has 74% of children being first borns. There are a lot of reasons why a poisson model probably isn't great, but it's worth pointing out that a model with more density near zero is probably likely and implies that first borns are more popular than the they look. 74% versus 80% isn't anything to write home about. Moreover, as Mz points out, only-children are a totally different case.

sasmith 17y ago
A Poisson distribution with a mean of 1.84 results in about 45% of children being first born. In fact, the best you can do with any distribution is 54%. For example, if there are 10k couples, then there will be 18.4k children born, at most 10k of which can be first born; and 10/18.4 = 54%. In fact, the only thing that matters for the distribution (once you know the mean) is the number of childless families, since they could have had a first born but didn't. I haven't been able to figure out where 74% comes from. Is there some way to sample on a per-family basis to come up with this? edit: spelling
- tel 17y ago
  More like a fundamentally stupid mistake of inverting my parameters when I checked the number, getting a result in tune with the article, and then not thinking it through at all. It'd be possible to have a whole great deal of families with 0.1st children, but that's just the egg on my face.
swwu 17y ago
Isn't Poisson rate-based, ie events over a fixed time period? I'm having trouble seeing where you got the rate from (children per lifetime? but that's hardly a "fixed time period") - all we have is a single number "children/household" with no time dimension. And most other distributions, ie other than the uniform I'm assuming and the Poisson you're using, require >1 parameters. Since we only have one piece of data (the mean) we would have to make assumptions with these distributions that make no more sense than simply assuming a uniform distribution to begin with. You'll have to excuse me for any incredibly stupid intuitive leaps; I haven't had a chance to wake up fully yet.

by tel 17y ago

sasmith 17y ago

A Poisson distribution with a mean of 1.84 results in about 45% of children being first born. In fact, the best you can do with any distribution is 54%. For example, if there are 10k couples, then there will be 18.4k children born, at most 10k of which can be first born; and 10/18.4 = 54%. In fact, the only thing that matters for the distribution (once you know the mean) is the number of childless families, since they could have had a first born but didn't. I haven't been able to figure out where 74% comes from. Is there some way to sample on a per-family basis to come up with this? edit: spelling

tel 17y ago
More like a fundamentally stupid mistake of inverting my parameters when I checked the number, getting a result in tune with the article, and then not thinking it through at all. It'd be possible to have a whole great deal of families with 0.1st children, but that's just the egg on my face.

swwu 17y ago

Isn't Poisson rate-based, ie events over a fixed time period? I'm having trouble seeing where you got the rate from (children per lifetime? but that's hardly a "fixed time period") - all we have is a single number "children/household" with no time dimension. And most other distributions, ie other than the uniform I'm assuming and the Poisson you're using, require >1 parameters. Since we only have one piece of data (the mean) we would have to make assumptions with these distributions that make no more sense than simply assuming a uniform distribution to begin with. You'll have to excuse me for any incredibly stupid intuitive leaps; I haven't had a chance to wake up fully yet.