ptsuite-package: ptsuite: Package for Pareto Parameter Estimation

In ptsuite: Tail Index Estimation for Power Law Distributions

Description

The ptsuite package provides functions to estimate parameters of Type I Pareto data. The details of the methods used and the equations implemented are given in the vignette. The package contains the following functions:

Estimator Functions

• Maximum Likelihood Estimator {alpha_mle}

• Weighted Least Squares Estimator {alpha_wls}

• Hill's Estimator {alpha_hills}

• Method of Moments Estimator {alpha_moment}

• Method of Percentiles Estimator {alpha_percentile}

• Method of Modified Percentiles Estimator {alpha_modified_percentile}

• Method of Geometric Percentiles {alpha_geometric_percentile}

• Least Squares Estimator {alpha_ls}

Other Functions

• Generate Pareto Data {generate_pareto}

• Estimates from all estimators {generate_all_estimates}

• Q-Q Plot to test for Pareto Distribution {pareto_qq_test}

• Pareto Test {pareto_test}

References

Newman MEJ (2005). "Power Laws, Pareto Distributions And Zipf's Law." Contemporary Physics, 46, 323-351.

Nair J, Wierman A, Zwart B (2019). "The Fundamentals Of Heavy Tails: Properties, Emergence, And Identification." http://users.cms.caltech.edu/ adamw/heavytails.html.

Pokorna M (2016). Estimation and Application of the Tail Index. Bachelor's thesis, Charles University in Prague, Faculty of Social Sciences, Institute of Economic Studies.

Hill B (1975). "A Simple General Approach To Inference About The Tail Of A Distribution."The Annals of Statistics, 3(5), 1163-1174.

Rytgaard M (1990). "Estimation In The Pareto Distribution." ASTIN Bulletin: The Journal Of The IAA, 20(2), 201-216.

Brazauskas V, Serfling R (2000). "Robust and Efficient Estimation Of The Tail Index Of A Single-Parameter Pareto Distribution." North American Actuarial Journal, 4, 12-27.

Bhatti SH, Hussain S, Ahmad T, Aslam M, Aftab M, Raza MA (2018). "Efficient estimation of Pareto model: Some modified percentile estimators." PLoS ONE, 13(5), 1-15.

Zaher HM, El-Sheik AA, El-Magd NATA (2014). "Estimation of Pareto Parameters Using a Fuzzy Least-Squares Method and Other Known Techniques with a Comparison." British Journal of Mathematics & Computer Science, 4(14), 2067-2088.

Gulati S, Shapiro S (2008). "Goodness-of-Fit Tests for Pareto Distribution." In F Vonta (ed.), Statistical Models and Methods for Biomedical and Technical Systems, chapter 19, pp. 259-274. Birkhauser Basel. ISBN 978-0-8176-4619-6. doi:10.1007/978-0-8176-4619-6.

ptsuite documentation built on May 1, 2019, 10:51 p.m.