Parameter Estimation
The likelihood function for the Pareto distribution parameters α and xm, given a sample x = (x1, x2, ..., xn), is
Therefore, the logarithmic likelihood function is
It can be seen that is monotonically increasing with, that is, the greater the value of, the greater the value of the likelihood function. Hence, since, we conclude that
To find the estimator for α, we compute the corresponding partial derivative and determine where it is zero:
Thus the maximum likelihood estimator for α is:
The expected statistical error is:
Read more about this topic: Pareto Distribution
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