 The univariate Pareto distribution has been extended to a multivariate Pareto distribution.The likelihood function for the Pareto distribution parameters "α" and "x"m, given an independent sample "x" = ("x"1, "x"2, ..., "xn"), is

Therefore, the logarithmic likelihood function is

It can be seen that formula_75 is monotonically increasing with "x"m, that is, the greater the value of "x"m, the greater the value of the likelihood function.Hence, since "x" ≥ "x"m, we conclude that

To find the estimator for "α", we compute the corresponding partial derivative and determine where it is zero