Modeling and simulation studies for some truncated discrete distributions generated by stable densities

Abstract

Some discrete distributions generated by stable densities (DGSDs) could be considered as models for describing phenomena arising in bioinformatics. Since probability mass and distribution functions are not in closed forms, simulation studies and real applications of these distributions have not been studied yet. To do this, we need to consider DGSDs as truncated, namely, truncated DGSDs (T-DGSDs). In this paper, some statistical properties of the T-DGSDs models are established. Based on the Monte Carlo method, limited-memory Broyden–Fletcher–Goldfarb–Shanno for bound-constrained optimization, and Nelder–Mead optimization algorithms, we do a simulation to estimate biases, mean square errors, and maximum likelihood estimations for the unknown parameters of the T-DGSDs. Moreover, we fit these T-DGSDs models with some real data sets in bioinformatics and then compare them to some frequency distributions.

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Acknowledgements

The author would like to thank the two anonymous referees for their valuable suggestions and comments. This work was supported by Quchan University of Technology under a grant number 7226.

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Correspondence to Davood Farbod.

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This work was supported by Quchan University of Technology under a grant number 7226.

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Farbod, D. Modeling and simulation studies for some truncated discrete distributions generated by stable densities. Math Sci (2021). https://doi.org/10.1007/s40096-021-00394-5

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Keywords

  • Discrete distributions generated by stable densities
  • Maximum likelihood estimation
  • Monte Carlo method

Mathematics Subject Classification

  • 62F10
  • 60E07
  • 62P10