Parameter Estimation in the Pareto Type-II Distribution Family (MLE)
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)
x |
a non-negative numeric vector |
s |
a-priori known scale parameter, s>0 or
|
smin |
lower bound for the scale parameter |
smax |
upper bound for the scale parameter |
tol |
the desired accuracy (convergence tolerance) |
Note that if s is not given, then
the maximum of the likelihood function might not exist
for some input vectors. This estimator may have a large mean squared error.
Consider using pareto2_estimate_mmse.
For known s, the estimator is unbiased.
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.
Other Pareto2: pareto2_estimate_mmse,
pareto2_test_ad,
pareto2_test_f, rpareto2
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