The distribution of for independent Poisson random variables with means is the Skellam distribution. Its characteristic function is , its mean is and its variance is . For equal means ,This is the fixed-time law of a symmetric Poisson difference process.
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The Skellam distribution is a probability distribution that describes the difference between two independent Poisson random variables. It is frequently used in various fields, particularly in statistics, telecommunications, and various types of counting processes.