Skip to main content
SpringerLink
Log in

A generalized semi-Pareto minification process

  • Regular Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

In this paper a generalization of the semi-Pareto autoregressive minification process of the first order is given. The necessary and sufficient condition for stationarity of the process is determined. It is shown that the process is ergodic and uniformly mixing. The joint survival function and the joint density function of the random variables X n+h and X n are determined. The extremes of the random variables X 1, X 2, ..., X n and the geometric extremes of random variables X 1, X 2, ..., X N are derived and their asymptotic distributions are discussed. The estimation of the parameters is discussed and some numerical results are given.

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

  • Ali MM, Marshall T, Babiker AG (2001) Analysis of incomplete durations with application to contraceptive use. J R Stat Soc Ser A 164:549–563

    Article  MATH  MathSciNet  Google Scholar 

  • Balakrishna N (1998) Estimation for the semi-Pareto processes. Commun Stat Theory Methods 27:2307–2323

    Article  MATH  MathSciNet  Google Scholar 

  • Balakrishna N, Jacob TM (2003) Parameter estimation in minification processes. Commun Stat Theory Methods 32:2139–2152

    Article  MATH  MathSciNet  Google Scholar 

  • Balakrishna N, Jayakumar K (1997) Bivariate semi-Pareto distributions and processes. Stat Pap 38:149–165

    Article  MATH  MathSciNet  Google Scholar 

  • Chiodo E, Mazzanti G (2004) The log-logistic model for reliability characterization of power system components subjected to random stress. SPEEDAM 2004, 16–18. June, Capri, Italy, pp. 239–244

  • Lewis PAW, McKenzie E (1991) Minification processes and their transformations. J Appl Probab 28:45–57

    Article  MATH  MathSciNet  Google Scholar 

  • Pillai RN (1991) Semi-Pareto processes. J Appl Probab 28:461–465

    Article  MATH  MathSciNet  Google Scholar 

  • Pillai RN, Jose KK, Jayakumar K (1995) Autoregressive minification processes and the class of distributions of universal geometric minima. J Indian Stat Assoc 33:53–61

    MathSciNet  Google Scholar 

  • Thomas A, Jose KK (2004) Bivariate semi-Pareto minification processes. Metrika 59:305–313

    Article  MathSciNet  Google Scholar 

  • Yeh HC, Arnold BC, Robertson CA (1988) Pareto processes. J Appl Probab 25:291–301

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Miroslav M. Ristić

Authors
  1. Miroslav M. Ristić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miroslav M. Ristić.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ristić, M.M. A generalized semi-Pareto minification process. Statistical Papers 49, 343–351 (2008). https://doi.org/10.1007/s00362-006-0017-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-006-0017-4

Keywords

Search

Navigation