1
$\begingroup$

Hello math geniuses! Compsci dude here.

I'm trying to model the price distribution of a category of goods, and figure a LogNormalDistribution would provide a good fit. The problem is, I don't know how to do this with the data I have available.

I have several data points available: C(x1) to C(xn). For a given x, C(x) is the cumulative percentage of all items cheaper than x dollars. That is, if C(x) = .5, x is the median.

Given points C(x1) to C(xn), how can I find the best fit Log Normal Distribution? I suppose the question really is: how do I find the best fit log normal cumulative distribution function for a given set of points, and how "good" will the fit be?

Thanks a lot for the help!

$\endgroup$
4
  • $\begingroup$ You might try math.stackexchange $\endgroup$
    – Will Jagy
    Jun 17, 2011 at 3:55
  • $\begingroup$ Is MathOverflow the more advanced version of math.stackexchange? Please excuse my ignorance. $\endgroup$
    – Franky
    Jun 17, 2011 at 3:58
  • $\begingroup$ Yes. From the faq, "MathOverflow's primary goal is for users to ask and answer research level math questions, the sorts of questions you come across when you're writing or reading articles or graduate level books." $\endgroup$
    – user5810
    Jun 17, 2011 at 4:17
  • $\begingroup$ Or even try stats.stackexchange.com, which is better for statistical questions $\endgroup$
    – David Roberts
    Jun 17, 2011 at 6:10

1 Answer 1

1
$\begingroup$

A simple estimation:

1) $y_i=\log(x_i)$

2) $\hat\mu = \sum_i y_i (F((y_i+y_{i+1})/2)-F((y_i+y_{i-1})/2)$

3) $\hat\sigma= (\sum_i y_i^2 (F((y_i+y_{i+1})/2)-F((y_i+y_{i-1})/2)) -\mu^2$.

Then $x \sim \mathrm{Lognormal}(\hat\mu,\hat\sigma)$

$\endgroup$
1
  • $\begingroup$ What function is F() ? $\endgroup$
    – Franky
    Jun 20, 2011 at 2:34

Not the answer you're looking for? Browse other questions tagged or ask your own question.