Advertisement

Triangular and Trapezoidal Distributions: Applications in the Genome Analysis

  • Luzia Gonçalves
  • Maria Antónia Amaral-Turkman
Article

Abstract

Recent research results indicate that classical triangular and trapezoidal distributions are having an increasing importance in many fields of science. This work brings a new application of triangular and trapezoidal distributions in the genome analysis, particularly, in the construction of physical mapping of linear and circular chromosomes. These distributions play an important role in a Bayesian approach devised to decide if two DNA fragments are nonoverlapped, partially overlapped or totally overlapped. Using triangular and trapezoidal distributions it is possible to obtain expressions for prior probabilities of these events based on fragment and genome lengths.

AMS Subject Classification

46N30 92D20 

Keywords

Triangular distribution Trapezoidal distribution Overlap probabilities Physical mapping 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdelrahman, M., Vijayakumar, V., Mahmoud, W., 2003. A methodology for multi-modal sensor fusion incorporating trend information. In Proceedings of the 31st International Conference on Computers and Industrial Engineering, 377–382.Google Scholar
  2. Alizadeh, F., Karp, R., Newberg, L., Weisser, D., 1995. Physical mapping of chromosomes: a combinatorial problem in molecular biology. Algorithmica, 13, 52–76.MathSciNetCrossRefGoogle Scholar
  3. Brown, S., 1999. An SAB report: Estimating uncertainties in radiogenic cancer risk. Technical Report EPA-SAB-RAC-99-008, United States Environmental Protection Agency, Science Advisor y Board Washington, DC.Google Scholar
  4. Gonçalves, L., 2004. Statistical Methodologies in Molecular Biology: Construction of Physical Maps. Ph.D. thesis, University of Lisbon, Portugal.Google Scholar
  5. Gonçalves, L., Zé-Zé, L., Pinheiro, H., Amaral-Turkman, M., 2005. Statistical aspects in physical mapping - application to the genome of O. oeni strain GM. Biometrics, 61, 481–487.MathSciNetCrossRefGoogle Scholar
  6. Johnson, N., Kotz, S., 1999. Non-smooth sailing or triangular distributions revisited after some 50 years. The Statistican, 48 (9), 179–187.Google Scholar
  7. Kececioglu, J., Shete, S., Arnold, J., 2000. Reconstructing distances in physical maps of chromosomes with nonoverlapping probes. In Proceedings of 4th ACM Conference on Computational Molecular Biology. 183–192.Google Scholar
  8. Kimmel, M., Gorlova, O.Y., 2003. Stochastic models of progression of cancer and their use in controlling cancer-related mortatality. International Journal of Applied Mathematics and Computer Science, 13, 279–287.Google Scholar
  9. Li, J., Wu, S., Huang, G., 2003. Handling temporal uncertainty in GIS domain: A fuzzy approach. In Symposium on Geospatial Theory, Processing and Applications, 1–6.Google Scholar
  10. Speed, T., Zhao, H., 2001. Chomosome maps. In Balding, D., Cannings, C., Bishop, M., (Eds.), Handbook of Statistical Genetics, 3–38, John Wiley and Sons.Google Scholar
  11. Tan, W., Cai, M., Zhou, R., 2003. Modified fuzzi point estimate method and its application to slope reliability analysis. Journal of University of Science and Techonolgy Beijing, 10, 5–10.Google Scholar
  12. van Drop, J., Kotz, S., 2002a. A novel extension of the triangular distribution and its parameter estimation. The Statistician, 51, 63–79.MathSciNetGoogle Scholar
  13. van Drop, J., Kotz, S., 2002b. The standard two-sided power distribution and its properties: With applications in financial engineering. The American Statistician, 56, 90–99.MathSciNetCrossRefGoogle Scholar
  14. van Drop, J., Kotz, S., 2003. Generalized trapezoidal distributions. Metrika, 58, 85–97.MathSciNetCrossRefGoogle Scholar
  15. van Drop, J., Kotz, S., 2004. Uneven two-sided power distribution: with applications in econometric models. Statistical Methods and Applications, 13, 285–313.MathSciNetCrossRefGoogle Scholar
  16. Yeh, R.-F., 1999. Statistical Issues in Genomic Mapping and Sequencing. PhD thesis, University of California, USA.Google Scholar

Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  • Luzia Gonçalves
    • 1
  • Maria Antónia Amaral-Turkman
    • 2
  1. 1.CEAUL and Epidemiology and Biostatistics Unit, Institute of Hygiene and Tropical MedicineUniversidade Nova de LisboaLisbonPortugal
  2. 2.CEAUL and Department of Statistics and Operations Research, Faculty of ScienceUniversity of LisbonLisbonPortugal

Personalised recommendations