In my book “Mathematical statistics with Applications”, written by Wackerly, it’s stated that there are two methods for parameterization of gamma distribution. The first one is k-theta and the second : alpha- beta. However, the difference is not defined.
What’s the difference between these two methods and what are the real-world applications of both methods?
The Wikipedia article gives both parameterizations. They are equivalent, and it is easy to convert between the two.
One difference is that if you run, e.g., gamma regression, expressing the functional form for one of the two parameterizations may be somewhat easier or better behaved. Further reading can be found at When to use gamma GLMs?