Skip to main content
SpringerLink
Log in

Hazard Rates Based on Isoprobability Contours

  • Chapter
Statistical Distributions in Scientific Work

Part of the book series: NATO Advanced study Institutes Series ((ASIC,volume 79))

Summary

A new “scalar” definition of a (contour) multivariate hazard rate based on variation of probability distribution across the isoprobability contours is motivated and described. Several examples involving specific multivariate distributions justifying the usefulness of this definition are presented. General structures of “constant” contour multivariate hazard rates as well as increasing contour multivariate hazard rates are described.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Basu, A.P. (1971). Bivariate failure rate. Journal of the American Statistical Association, 66, 103–104.

    Article  MATH  Google Scholar 

  • Bildikar, S., Patil, G.P. (1968). Multivariate exponential type distributions. Annals of Mathematical Statistics, 39, 1316–1326.

    Article  MathSciNet  MATH  Google Scholar 

  • Block, H.W. (1973). Monotone hazard and failure rates for absolutely continuous multivariate distributions. Department of Mathematics Research Report #73–20, University of Pittsburgh. Also Naval Research Logistics Quarterly, 24, 1977, 627–638.

    Google Scholar 

  • Brindley, E.C., Thompson, W.A. (1972). Dependence and aging aspects of multivariate survival. Journal of the American Statistical Association, 67, 822–830.

    Article  MathSciNet  MATH  Google Scholar 

  • Day, N.E. (1969). Linear and quadratic discrimination in pattern recognition. IEEE Transactions on Information Theory, 15, 419–421.

    Article  MATH  Google Scholar 

  • Farlie, D.J.G. (1960). The performance of some correlation coefficients for a general bivariate distribution. Biometrika, 47, 307–323.

    MathSciNet  MATH  Google Scholar 

  • Fraser, D.A.S. (1963). The Structure of Inference. Wiley, New York.

    Google Scholar 

  • Fréchet, M. (1951). Sur les tableaux de correlation dont les marges sont données. Annales de l’Universite de Lyon, Section A, Ser. 3, 14, 53–77.

    Google Scholar 

  • Freund, R.J. (1961). A bivariate extension of the exponential distribution. Journal of the American Statistical Association, 56, 971–977.

    Article  MathSciNet  MATH  Google Scholar 

  • Fu, J.C. (1974). On non–uniqueness of ancillary statistics. Communications in Statistics, 3, 1093–1100.

    Article  Google Scholar 

  • Goodman, I., Kotz, S. (1973). Multivariate θ–generalized normal distributions. Journal of Multivariate Analysis, 3, 204–219.

    Article  MathSciNet  MATH  Google Scholar 

  • Gumbel, E.J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55, 698– 707.

    Article  MathSciNet  MATH  Google Scholar 

  • Harris, R. (1970). A multivariate definition for increasing hazard rate functions. Annals of Mathematical Statistics, 41, 713–717.

    Article  MathSciNet  MATH  Google Scholar 

  • Higgins, J.J. (1975). A geometrical method of constructing multivariate densities and some related inferential procedures. Communications in Statistics, 4, 955–966.

    Article  MathSciNet  Google Scholar 

  • Johnson, N.L., Kotz, S. (1972). Distributions in Statistics, Continuous Multivariate Distributions. Wiley, New York.

    MATH  Google Scholar 

  • Johnson, N. L., Kotz, S. (1975a). On some generalized Farlie– Gumbel–Morgenstern distributions. Communications in Statistics, 4, 415–428.

    Article  MathSciNet  Google Scholar 

  • Johnson, N. L., Kotz, S. (1975b). A vector multivariate hazard rate. Journal of Multivariate Analysis, 5, 53–66.

    Article  MathSciNet  MATH  Google Scholar 

  • Marshall, A. W. (1975). Some comments on the hazard gradient. Stochastic Processes and their Applications, 3, 293–300.

    Article  MathSciNet  MATH  Google Scholar 

  • Marshall, A. W., Olkin, I. (1967a). A generalized bi–variate exponential distribution. Journal of Applied Probability, 4, 291–302.

    Article  MathSciNet  MATH  Google Scholar 

  • Marshall, A.W., Olkin, I. (1967b). A multivariate ex–ponential distribution. Journal of the American Statistical Association, 62, 30–44.

    Article  MathSciNet  MATH  Google Scholar 

  • Morgenstern, D. (1956). Einfache Beispiele zweidimensionaler Verteilungen. Mitteilingsblatt für Mathematische Statistik, 8, 234–235.

    MathSciNet  Google Scholar 

  • Sagrista, S.N. (1952). On a generalization of Pearson’s curves to the two dimensional space. Trabajos de Estadistica, 3, 273–314.

    Article  MathSciNet  MATH  Google Scholar 

  • Simoni, de S. (1968). Su una estensione delle curve normali di ordina r alle variabili doppie. Statistica (Bologna), 28, 151–170.

    Google Scholar 

  • Styen, H. S. (1960). On regression properties of multivariate probability functions of Pearson’s type. Proceedings of the Royal Academy of Science, Amsterdam, 63, 302–311.

    Google Scholar 

  • Uven, M. J. van. (1947–1948). Extension of Pearson’s probability distributions to two variables, I-IV. Proceedings of the Royal Academy of Sciences, Amsterdam, 50, 1063–1070, 1252–1264; 51, 41–52, 191–196.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Naval Research Laboratory, Washington, D.C, 20375, USA

    I. R. Goodman

  2. University of Maryland, College Park, Maryland, 20742, USA

    Samuel Kotz

Authors
  1. I. R. Goodman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Samuel Kotz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistics, The pennsylvania State University, University Park, Pennsylvania, USA

    Charles Taillie  & Ganapati P. Patil  & 

  2. Instituto di Calcolo delle Probabilità, Facoltà di Scienze Statistische Demografiche e Attuariali, Università degli Studi di Roma, Italy

    Bruno A. Baldessari

Rights and permissions

Reprints and permissions

Copyright information

© 1981 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Goodman, I.R., Kotz, S. (1981). Hazard Rates Based on Isoprobability Contours. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8552-0_23

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-8552-0_23

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8554-4

  • Online ISBN: 978-94-009-8552-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation