Skip to main content
SpringerLink
Log in

Characterizations of Certain Continuous Distributions

  • Chapter
  • First Online:
Multiscale Signal Analysis and Modeling

  • 1532 Accesses

Abstract

In designing a stochastic model for a particular modeling problem, an investigator will be vitally interested to know if their model fits the requirements of a specific underlying probability distribution. To this end, the investigator will vitally depend on the characterizations of the selected distribution. The Amoroso, SSK (Shakil–Singh–Kibria), SKS (Shakil–Kibria–Singh), SK (Shakil–Kibria), and SKS-type distributions have been suggested to have potential applications in modeling and are characterized here based on either a simple relationship between two truncated moments or a truncated moment of a function of the first order statistic or of a function of the nth order statistic, the two more interesting order statistics. We also present a characterization of SKS-type distribution based on the conditional expectation of adjacent generalized order statistics.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ahsanullah M (1973) A characterization of the power function distribution. Commun Stat 2:259–262

    MathSciNet  MATH  Google Scholar 

  2. Ahsanullah M (2004) On characterizations of the uniform distribution based on functions of order statistics. Commun Stat Theor Methods 33 :2921–2928

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahsanullah M, Hamedani GG (2007) Certain characterizations of the power function and beta distribution based on order statistics. J Stat Theor Appl 6 :220–225

    MathSciNet  Google Scholar 

  4. Asadi M, Ebrahimi N, Hamedani GG, Soofi E (2004) Maximum dynamic entropy models. J Appl Probab 41:379–390

    Article  MathSciNet  MATH  Google Scholar 

  5. Asadi M, Ebrahimi N, Hamedani GG, Soofi E (2005) Minimum dynamic discrimination information models. J Appl Probab 42:643–660

    Article  MathSciNet  MATH  Google Scholar 

  6. Burr IW (1942) Cumulative frequency functions. Ann Math Stat 13 :215–232

    Article  MathSciNet  MATH  Google Scholar 

  7. Crooks GE (2010) The Amoroso distribution. arXiv:1005.3274v1 [math.ST]

    Google Scholar 

  8. Galambos J, Kotz S (1978) Characterizations of probability distributions. In: A unified approach with an emphasis on exponential and related models, Lecture Notes in Mathematics, vol 675. Springer, Berlin

    Google Scholar 

  9. Glänzel W (1987) A characterization theorem based on truncated moments and its application to some distribution families. Math Stat Probab Theor (bad Tatzmannsdorf, 1986):75–84

    Google Scholar 

  10. Glänzel W (1988) A characterization of the normal distribution. Studia Sci Math Hungar 23:89–91

    MathSciNet  MATH  Google Scholar 

  11. Glänzel W, Hamedani GG (2001) Characterizations of univariate continuous distributions. Studia Sci Math Hungar 37:83–118

    MathSciNet  MATH  Google Scholar 

  12. Glänzel W, Telcs A, Schubert A (1984) Characterization by truncated moments and its application to Pearson-type distributions. Z Wahrsch Verw Gebiete 66:173–183

    Article  MathSciNet  MATH  Google Scholar 

  13. Hamedani GG (2002) Characterizations of univariate continuous distributions II. Studia Sci Math Hungar 39:407–424

    MathSciNet  MATH  Google Scholar 

  14. Hamedani GG (2006) Characterizations of univariate continuous distributions III. Studia Sci Math Hungar 43:361–385

    MathSciNet  MATH  Google Scholar 

  15. Hamedani GG (2010) Characterizations of continuous univariate distributions based on the truncated moments of functions of order statistics. Studia Sci Math Hungar 47:462–484

    MathSciNet  MATH  Google Scholar 

  16. Hamedani GG (2011) Characterizations of the Shakil-Kibria-Singh distribution 40:201–207

    MathSciNet  Google Scholar 

  17. Hamedani GG, Ahsanullah M, Sheng R (2008) Characterizations of continuous univariate distributions based on truncated moment of first order statistic. Aligarh J Stat 28:75–81

    MathSciNet  Google Scholar 

  18. Johnson NI, Kotz S (1970) Distributions in statistics. Continuous univariate distributions, vols 1 and 2. Houghton Miffin Co., Boston, Mass

    Google Scholar 

  19. Kamps U (1995) A concept of generalized order statistics. In: Teubner BG, Stuttgart Teubner Skripten zur Mathematischen Stochastik. [Teubner Texts on Mathematical Stochastics]

    Google Scholar 

  20. Kotz S, Shanbhag DN (1980) Some new approaches to probability distributions. Adv Appl Probab 12:903–921

    Article  MathSciNet  MATH  Google Scholar 

  21. McDonald JB (1984) Some generalized functions for the size distribution of income. Econometrica 52:647–663

    Article  MATH  Google Scholar 

  22. Pearson K, (1895) Contributions to the mathematical theory of evolution. Skew variation in homogeneous material. London Phil Trans Ser A 186:393–415; Lond R S Proc 57:257–260

    Article  Google Scholar 

  23. Shakil M, Kibria BM (2010) On a family of life distributions based on generalized Pearson differential equation with applications in health statistics. J Stat Theor Appl 9:255–281

    MathSciNet  Google Scholar 

  24. Shakil M, Kibria BM, Singh JN (2010) A new family of distributions based on the generalized Pearson differential equation with some applications. Austrian J Stat 39:259–278

    Google Scholar 

  25. Shakil M, Singh JN, Kibria BM (2010) On a family of product distributions based on the Wittaker functions and generalized Pearson differential equation. Pakistan J Stat 26:111–125

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI, 53201-1881, USA

    G. G. Hamedani

Authors
  1. G. G. Hamedani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. G. Hamedani .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Ohio University, Ohio University 1, Athens, 45701, Ohio, USA

    Xiaoping Shen

  2. , Department of Mathematical Sciences, DePaul University, North Kenmore Avenue 2320, Chicago, 60614, Illinois, USA

    Ahmed I. Zayed

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer New York

About this chapter

Cite this chapter

Hamedani, G.G. (2013). Characterizations of Certain Continuous Distributions. In: Shen, X., Zayed, A. (eds) Multiscale Signal Analysis and Modeling. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4145-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-4145-8_13

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-4144-1

  • Online ISBN: 978-1-4614-4145-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation