ignore previous post
OK I think I am somewhat closer.
Using the result for the change of variables of a distribution shown about half way down this page:http://en.wikipedia.org/wiki/Probabilit ... y_function
If the probability density function of a random variable X is given as
, it is possible to calculate the probability density function of
using the formula
Thus the lognormal distibution with params
and we want to transform to
which they describe as the lognormal form in which
Taking the change of variable to be
this effectively cancels out the
term in the original pdf when you take it out of the square root and place it in the numerator.
and taking the inverse
and the derivative is
and so applying the change of variable formula above.
where now the transformed variable
is used in
this cancels with the
term in the denomiator of the first fraction in the original pdf leaving
which is the solution we are looking for apart from the factor of
can you see where that might cancel?
So the formula looks correct but I am not getting correct scaling when I apply to data.
My question is:
1.) When the variables are plotted in a log-log plot (as in fig 3a of the original paper), can I take
to be equal to the value of the peak probability
If so should I then take
figure seems to work much better giving nearly right answers? But intuitively it seems wrong? The only place
scale is used is in the log-log plot?
2.) Similarly they say that
should be the width of the parabola on a log-log scale? I simply take this to mean the difference in the values of
when at the maximum and minimum probabilities respectively. Is this correct?
If so and the similar to part 1 should I use this value expressed on a