Skip to main content
  • 1152 Accesses

Abstract

The analysis and interpretation of directional data requires specific data representations, descriptions and distributions. Directional data occurs in many areas, namely the Earth Sciences, Meteorology and Medicine. Note that directional data is an “interval type” data: the position of the “zero degrees” is arbitrary. Since usual statistics, such as the arithmetic mean and the standard deviation, do not have this rotational invariance, one must use other statistics. For example, the mean direction between 10° and 350° is not given by the arithmetic mean 180°.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Reference

  • Fisher NI, Best DJ (1984) Goodness-of-Fit Tests for Fisher’s Distribution on the Sphere. Austral. J. Statist., 26: 142–150.

    Google Scholar 

  • Fisher NI, Lewis T, Embleton BJJ (1987) Statistical Analysis of Spherical Data. Cambridge University Press.

    Google Scholar 

  • Greenwood JA, Durand D (1955) The Distribution of Length and Components of the Sum of n Random Unit Vectors. Ann. Math. Statist., 26: 233–246.

    Google Scholar 

  • Gumbel EJ, Greenwood JA, Durand D (1953) The Circular Normal Distribution: Theory and Tables. J. Amer. Statist. Assoc., 48: 131: 152.

    MathSciNet  Google Scholar 

  • Hill GW (1976) New Approximations to the von Mises Distribution. Biometrika, 63: 676–678.

    Article  Google Scholar 

  • Hill GW (1977) Algorithm 518. Incomplete Bessel Function Io: The Von Mises Distribution. ACM Tr. Math. Software, 3: 270–284.

    Article  Google Scholar 

  • Jammalamadaka SR (1984) Nonparametric Methods in Directional Data Analysis. In: Krishnaiah PR, Sen PK (eds), Handbook of Statistics, vol. 4, Elsevier Science B.V., 755–770.

    Google Scholar 

  • Kanji GK (1999) 100 Statistical Tests. Sage Publications Ltd.

    Google Scholar 

  • Mardia KV, Jupp PE (2000) Directional Statistics. John Wiley and Sons, Inc.

    Google Scholar 

  • Schou G (1978) Estimation of the Concentration Parameter in von Mises Distributions. Biometrika, 65: 369–377.

    MathSciNet  MATH  Google Scholar 

  • Upton GJG (1973) Single-Sample Test for the von Mises Distribution. Biometrika, 60: 8799.

    Article  MathSciNet  Google Scholar 

  • Upton GJG (1986) Approximate Confidence Intervals for the Mean Direction of a von Mises Distribution. Biometrika, 73: 525–527.

    Article  MathSciNet  Google Scholar 

  • Watson GS, Williams EJ (1956) On the Construction of Significance Tests on the Circle and the Sphere. Biometrika, 48: 344–352.

    MathSciNet  Google Scholar 

  • Wilkie D (1983) Rayleigh Test for Randomness of Circular Data. Appl. Statist., 7: 311–312.

    Article  Google Scholar 

  • Wood, ATA (1994) Simulation of the von Mises Fisher Distribution. Comm. Statist. Simul., 23: 157–164.

    Google Scholar 

  • Zar JH (1996) Biostatistical Analysis. Prentice Hall, Inc.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Marques de Sá, J.P. (2003). Directional Data. In: Applied Statistics Using SPSS, STATISTICA and MATLAB. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05804-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-05804-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-05806-0

  • Online ISBN: 978-3-662-05804-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics