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.