pareto2_estimate_mle {agop}

Parameter Estimation in the Pareto Type-II Distribution Family (MLE)

Description

Finds the maximum likelihood estimator of the Pareto Type-II distribution's shape parameter k and, if not given explicitly, scale parameter s.

Usage

pareto2_estimate_mle(
  x,
  s = NA_real_,
  smin = 1e-04,
  smax = 20,
  tol = .Machine$double.eps^0.25
)

Arguments

x

a non-negative numeric vector

s

a-priori known scale parameter, s>0 or NA if unknown (default)

smin

lower bound for the scale parameter

smax

upper bound for the scale parameter

tol

the desired accuracy (convergence tolerance)

Details

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.

Value

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.

See Also

Other Pareto2: pareto2_estimate_mmse(), pareto2_test_ad(), pareto2_test_f(), rpareto2()