Explanation from notebook pasted below for future reference:
Gamma-hurdle parameter estimation
Until present, we have been estimating the parameters of the gamma-hurdle distribution as follows. Suppose we observe , draws from a gamma-hurdle distribution.
This method is very computationally favorable, as it requires only the sum, sum of squares, n, and nnz to estimate all three parameters. These estimates were determined by matching mean and variance to those of a gamma distribution given certain parameters, rather than by a more standard method.
A standard way to estimate the parameters of statistical distributions given observations is maximum likelihood estimation (MLE). Using MLE, we obtain the same estimate for and the same relationship between and (that is, ), but a different estimate for itself. The MLE estimates are as follows
This notebook attempts to determine whether our moment-matching estimates are similar to the MLE estimates.
Explanation from notebook pasted below for future reference:
Gamma-hurdle parameter estimation
Until present, we have been estimating the parameters of the gamma-hurdle distribution as follows. Suppose we observe
, draws from a gamma-hurdle distribution.
This method is very computationally favorable, as it requires only the sum, sum of squares,
n, andnnzto estimate all three parameters. These estimates were determined by matching mean and variance to those of a gamma distribution given certain parameters, rather than by a more standard method.A standard way to estimate the parameters of statistical distributions given observations is maximum likelihood estimation (MLE). Using MLE, we obtain the same estimate for
and the same relationship between 
and 
(that is, 
), but a different estimate for 
itself. The MLE estimates are as follows
This notebook attempts to determine whether our moment-matching estimates are similar to the MLE estimates.