The expression, y = a*x^(b) * e^(lambda*x), is the gamma distribution. Please refer to the following documentation for the gamma distribution:
You can use the "gamfit" or "fitdist" function to fit the above distribution via maximum likelihood, rather than fitting "a", "b", and "lambda" separately, as they cannot be selected independently. It is not considered as a valid probability density unless "a" is a specific function of "b" and "lambda". Please refer to the following link for more information on using the "gamfit" and "fitdist" functions respectively:
For the power law distribution, you can use the "mle" function, but you need to write a function that computes the "pdf" or "logpdf" of the power law distribution. Please refer to the attached example, "powerLawExample.m", that demonstrates how to use the "mle" function by writing a function that computes the "logpdf" of the power law distribution.
