I want to compute the parameters mu and lambda for the Inverse Gaussian Distribution given the CDF.
By 'given the CDF' I mean that I have given the data AND the (estimated) quantile for the data I.e.
Quantile - Value
0.01 - 10
0.5 - 12
0.7 - 13
Now I want to find out the inverse gaussian distribution for this data so that I can e.g. Look up the quantile for value 11 based on my distribution.
How can I find out the values mu and lambda?
The only solution I can think of is using Gradient descent to find the best mu and lambda using RMSE as an error measure.
Isn't there a better solution?
Comment: Matlab's MLE-Algorithm is not an option, since it does not use the quantile data.
As all you really want to do is estimate the quantiles of the distribution at unknown values and you have a lot of data points you can simply interpolate the values you want to lookup.
quantile_estimate = interp1(values, quantiles, value_of_interest);
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