A Modified Chi-Squared Goodness-of-Fit Test for the Three-Parameter Gamma Distribution with Unknown Parameters

A modified chi-squared goodness-of-fit test was created for the gamma distribution in the case where all three parameters must be estimated from the sample. Critical values are generated using a Monte Carlo simulation procedure with 5000 repetitions each. Random samples of 8 different sizes were drawn from gamma distributions with shape parameters 1, 1.5, 2., and 2.5. The shape, scale, and location parameters were then estimated from each sample, using an iterative technique combining the maximum likelihood and minimum distance methods, enabling, computation of the chi-squared statistics and critical values. The same process is used to generate random samples, parameter estimates, and chi- squared statistics from 10 alternate distributions as a check on the power of this chi-squared goodness-of-fit test. The goodness-of-fit tests were executed by comparing the chi-squared statistics from the alternate distributions with the gamma critical values, allowing the power to be calculated against each alternate distribution.... Goodness of Fit, Chi-Squared Statistic, Gamma Distribution, Maximum Likelihood, Minimum Distance.