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The generalized Poisson distribution is a distribution which approximates various forms of mixtures of Poisson distributions. The mean and variance of the generalized Poisson distribution, which are simple functions of the two parameters of the distribution, are more useful than the original parameters in test data analysis. Therefore, we adopted two types of transformations of parameters. The first model has new parameters of mean and standard deviation. The second model contains new parameters of mean and variance/mean. An example indicates that the transformed parameters are convenient to understand the properties of data.

Transformations of parameters in the generalized Poisson distribution for test data analysis.