An Application of Archimedean Copulas for Meteorological Data

Abstract

This paper suggests a goodness-of-fit test for monthly lowest and highest air temperature records from years 1951 to 2005 in Tehran -Iran(648 data),  based on the classical chi-square statistic. After remembering some notes about Archimedean Copulas, we will see (for this data), which families of Copulas are suitable. Then we characterize interval of suitable theta, and also figure out the best theta

Keywords

• Archimedean Copulas
• Goodness-of-fit test
• Meteorological data

References

1. Ali, MM,. Mikhail, NN,.Haq, MS,. A class of bivariate distributions including the bivariate logistic. Multivariate Anal. 8: 405-412 (1978).
2. Çelebioğlu, S,. Archimedean Copulas And An Application, S Ü Fen Ed Fak Fen Derg , 22 (2003) 43- 52, KONYA.
3. Clayton, DG,. A model for association in bivariate life tables and its applicationin epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65: 141-151(1978).
4. Conway, DA,. Plackett family of distributions. In: Kotz S. Johnson NL (eds). Encyclopedia of Statistical Sciences, Vol 7. Wiley, New York, 1-5 (1986).
5. Cook RD, Johnson ME,. A family of distributions for modeling non-elliptically symmetric multivariate data. J. Roy Statist. Soc. SerB 43:210-218(1981).
6. Cook RD,. Johnson ME,.Generalized Burr-Pareto- logistic distributions withapplications to a uranium exploration data set. Technometrics 28:123- 131(1986).
7. Cox DR,. Oakes D,. Analysis of Survival Data. Chapman and Hall, London (1984).
8. Emura T,. LinCW,. Wang W,. A goodness-of-fit test for Archimedean copula models in the presence ofright censoring. Computational Statistics and Data Analysis, (2008).

9. Frank MJ,. On the simultaneous associativity of ( ) and ( ) . Aequationes Math 19:194-226 (1979).
10. Genest,C., Rivest L.P,. Statistical Inference Procedures for Bivariate Archimedean Copulas. Journal of the American Statistical Association, Vol. 88, No. 423, pp. 1034-1043 (1993).
11. Genest C,.MacKay J,. Copules archimédien nesetfamilles de loisbidimension nellesdont les margessontdonnées. Canad. J. Statist., 14:145-159 (1986a).
12. Genest C,. MacKay J,. The joy of copulas: Bivariate distributions with uniform marginals. Amer. Statist. 40:280-285 (1986b).
13. Gumbel EJ,. Distributions des valeursextrêmes en plusiers dimensions. PublInst. Statist. Univ. Paris 9:171-173 (1960b).
14. Hougaard P,. A class of multivariate failure time distributions. Biometrika, 73:671-678 (1986).
15. Hutchinson TP,. Lai CD,. Continuous Bivariate Distributions, Emphasising Applications. Rumsby Scientific Publishing, Adelaide (1990).
16. I.R. OF Iran meteorological organization (IRIMO).
17. Joe, H,. Multivariate Models and Dependence Concepts. Chapman & Hall, London (1997).
18. Nelsen, R.B,. An Introduction to Copulas, Springer, New York (1999).
19. Plackett RL,. A class of bivariate distributions. J Amer. Statist. Assoc, 60:516-522(1965).