Branching Processes Engine - R2


Version: 1.1.0


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DESCRIPTION:
The aim of this system is to give a simple and flexible way for demonstration of the properties and behaviour of the branching processes and for estimation of their parameters in education as well as estimation of the parameters of real data samples in scientific research.

The system includes a package of functions for estimation of the parameters of a classical Bienayme - Galton - Watson branching processes as well as processes with immigration. The estimation of the parameters is based on the information about the entire family tree.

The package is written in MATLAB, but the main functionality of the package can be run on Octave.

The package has its own engine for generating the entire family tree of the process in the form of vector of parent pointers. When estimating the parameters from external data, they should have the same format as generated.

In addition, there is an executable program with GUI which allows an user-friendly usage (needs MATLAB R13).

More about the package (instalation, ussage and included functions) can be found in included README file.

AUTHORS:
Dimitar Atanasov
datanasov@fmi.uni-sofia.bg

Vessela Stoimenova
stoimenova@fmi.uni-sofia.bg

LICENSE:
The package is under the CC-GNU LGPL.
You may use, copy or redistribute this package free if name of the package, names and e-mail addresses of the authors are cited.

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REFERENCES:

  1. Dion J.P.(1993) Statistical Inference for descrete time branching processes. Lecture Notes. 7th International Summer School on Probability Theory and Mathematical Statistics. ed. A. Obretenov, V.T. Stefanov. 60 - 121.
  2. Dion J.P., Yanev, N.M. (1991). Limiting Distributions of a Galton-Watson Branching Process with a Random Number of Ancestors. Compt. rend. Acad. bulg. Sci. 44, No 3, 23-26.
  3. Dion J.P., Yanev, N.M. (1994) Statistical Inference for Branching Processes with an Increasing Number of Ancestors. J. Statistical Planning & Inference.39. 329 - 359.
  4. Dion J.P., Yanev, N.M. (1997). Limit Theorems and Estimation Theory for Branching Processes with an Increasing Random Number of Ancestors. J. Appl. Prob. 34,309-327.
  5. Guttorp P. (1991). Statistical Inference for Branching Processes. John Wiley & Sons.
  6. Heyde C.C. (1974). On estimating the variance of the offspring distribution in a simple branching process. Adv. Appl. Prob 3. 421-433.
  7. Heyde C.C., Seneta E. (1972). Estimation theory for growth and immigration rates in a multiplicative process. J. Appl. Prob 9. 235-256.
  8. Stoimenova V. (2005). Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors. Serdica Math. J. 31. 243 - 262.
  9. Stoimenova V., Atanasov D., Yanev N. (2004a) Robust Estimation and Simulation of Branching Processes. C. R. Acad. Bulg. Sci. 57. No 5. 19 - 22.
  10. Stoimenova V., Atanasov D., Yanev N. (2004b) Simulation and Robust Modiffication of Estimates in Branching Processes. Pliska Stud. Math. Bulgar. 16. 259 - 271.
  11. Stoimenova V., Atanasov D., Yanev N. (2005) Algorithms for Generation and Robust Estimation of Branching Processes with Random Number of Ancestors. Math. & Education in Math. Proceedings of 34 Spring Conference of UBM. 196 - 201.
  12. Wei C.Z., Winnicki J. (1989). Some asymptotic results of branching processes with immigration. Ann. Statist. 31. 261 - 282.
  13. Wei C.Z., Winnicki J. (1990). Estimations of the means in the branching processes with immigration. Ann. Statist. 18. 1757 - 1773.
  14. Winnicki J. (1988). Estimation Theory of the Branching Processes with Immigration. Contemporary Mathematics. 80. 301 - 323.