Skip to main content
SpringerLink
Log in

A product Pareto distribution

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

The Pareto distributions are becoming increasing prominent in several applied areas. In this note, a new Pareto distribution is introduced. It takes the form of the product of two Pareto probability density functions. Various structural properties of this distribution are derived, including its cumulative distribution function, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, method of moments estimates, maximum likelihood estimates and the Fisher information matrix. The calculations involve the use of several special functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Gradshteyn IS and Ryzhik IM (2000). Table of integrals, series and products, 6th edn. Academic, San Diego

    MATH  Google Scholar 

  • Kleiber C and Kotz S (2003). Statistical size distributions in economics and actuarial sciences. Wiley, New York

    MATH  Google Scholar 

  • Leadbetter MR, Lindgren G and Rootzén H (1987). Extremes and related properties of random sequences and processes. Springer, New York

    Google Scholar 

  • Prudnikov AP, Brychkov YA and Marichev OI (1986). Integrals and series, vol. 1–3. Gordon and Breach Science Publishers, Amsterdam

    Google Scholar 

  • Rényi A (1961) On measures of entropy and information. In: Proceedings of the 4th Berkeley symposium on mathematical statistics and probability, vol. I. University of California Press, Berkeley, pp 547–561

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M60 1QD, UK

    Saralees Nadarajah

  2. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Arjun K. Gupta

Authors
  1. Saralees Nadarajah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arjun K. Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saralees Nadarajah.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nadarajah, S., Gupta, A.K. A product Pareto distribution. Metrika 68, 199–208 (2008). https://doi.org/10.1007/s00184-007-0152-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-007-0152-5

Keywords

Search

Navigation