# Log Normal Distribution best fit

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