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Compsci dude here.

I'm trying to model the price distribution of a category of goods, and figure a Log Normal Distribution 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: $C(x_1)$ to $C(x_n)$. 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 $C(x_1)$ to $C(x_n)$, 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.

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"Best" raises the question of "in what sense"? The answer is usually informed by the nature of the sampling variation in the data $C(x_i)$. What can you say about how the $C(x_i)$ are measured and the uncertainties of those measurements? How are the $x_i$ chosen? Another key element of a good solution is attention to how the answer will be used. What will you be doing with the estimated lognormal parameters? What is the cost of making errors in the estimation? –  whuber Jun 17 '11 at 15:40

1 Answer 1

If you believe in the log normal distribution, there are only two parameters. I would do a 2 dimensional fit to your cumulative distribution. Routines are available at Numerical Recipes, chapter 10, (old versions are free).

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This is an option, though there must be a non heuristic approach. –  franky Jun 17 '11 at 4:25
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If you have data that comes without a scientific model of where it comes from, why should there be a non-heuristic approach? There are distributions arbitrarily close to log normal, so no amount of data can prove the distribution is log normal. You can only prove (at a level of confidence) that it is not. –  Ross Millikan Jun 17 '11 at 4:31

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