Finds the maximum likelihood estimator of the Pareto Type-II distribution's shape parameter \(k\) and, if not given explicitly, scale parameter \(s\).
pareto2_estimate_mle(x, s = NA_real_, smin = 1e-04, smax = 20,
tol = .Machine$double.eps^0.25)a non-negative numeric vector
a-priori known scale parameter, \(s>0\) or
NA if unknown (default)
lower bound for the scale parameter to look for
upper bound for the scale parameter to look for
the desired accuracy (convergence tolerance)
Returns a numeric vector with the following named components:
k - estimated parameter of shape
s - estimated (or known, see the s argument) parameter of scale
or c(NA, NA) if the maximum of the likelihood function
could not be found.
Note that if \(s\) is not given, then
the maximum of the likelihood function may not exist
for some input vectors. This estimator may have large mean squared error.
Consider using pareto2_estimate_mmse.
For known \(s\), the estimator is unbiased.
Other Pareto2: pareto2_estimate_mmse,
pareto2_test_ad,
pareto2_test_f, rpareto2