**GENEALOGY-DNA-L Archives**

From:"Bonner, Gregg" <>Subject:[DNA] Poisson vs. othersDate:Sat, 6 Jul 2002 06:40:01 -0400Hi Folks,

John wrote:

If you assume an average rate of mutation PER GENERATION, the Poisson

distribution is a decent approximation in the long run, but the binomial

distribution is the EXACT representation for all cases. I cannot see a

motivation to use an approximation when the exact formula is so simple

and easy.

My reply:

The most obvious motivation to use Poisson, rather than exact binomial is

that exact binomial will be impossible to use as a practical matter in many

cases.

Take my Lentz/Lance scenario, where we test 12 markers through a total of 36

transmission events. The exact binomial in this case would be:

p (observing k mutations out of n [in this case, 432] chances) =

[n!/k!(n-k)!][(p^k)(q^{n-k})]

Rather than plug in any number of hypothetically observed mutations, and the

other values, I will only point out that the first part will crash many

calculators/computers - try getting a value for 432 factorial. I know that

generally older calculaters max out at 69 factorial, because 70 factorial

puts the value at greater than 1E100 (1.198E100). The important part of that

is that that is when the exponent crosses over into 3 digits, whereas 69

factorial is 1.711E98. On my home computer, I can calculate factorial up to

170 (7.257E306). So my home computer can not get me even near the required

n=432, and my sample is small at only 5 people. I realize that people can

call someone up with a bigger, better computer to get factorial values, but

this is not terribly convenient.

Since Poisson is p=(e^-np)(np^k)/k!, it has no such large factorials to

handle, unless you really expect to have a dataset that shows greater than

69 mutations.

Cheers,

Gregg

**This thread:**

**[DNA] Poisson vs. others by "Bonner, Gregg" <>**- Re: [DNA] Poisson vs. others by "John F. Chandler" <>

- RE: [DNA] Poisson vs. others by "Bonner, Gregg" <>

- Re: [DNA] Poisson vs. others by "John F. Chandler" <>

- Re: [DNA] Poisson vs. others by James W Green III <>
- Re: [DNA] Poisson vs. others by "Michael O'Rourke" <>

- Re: [DNA] Poisson vs. others by "John F. Chandler" <>