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Statistical Fundamentals

In: Modelling with the Master Equation

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  • Günter Haag

    (University of Stuttgart, Institute of Theoretical Physics II)

Abstract

The primary objective of this chapter is to provide some statistical fundamentals needed for the understanding of the modelling framework of the Master equation. The starting point will be the usual classification of systems as deterministic or probabilistic. For the description of the space-time dynamics of any system some mathematical indicators and functions are indispensable. Therefore, beside mean values and moments and the definition of correlation functions and the Wiener-Chinchin theorem, the characteristic function and the generating function are presented. Five examples of important statistical distributions, namely, the binomial distribution, the Poisson distribution, the normal distribution, the Gumbel distribution and the Pareto distribution are further discussed. The content of this chapter will be used in the coming examples and applications of the Master equation and can be seen as a tool box for statistical applications.

Suggested Citation

  • Günter Haag, 2017. "Statistical Fundamentals," Springer Books, in: Modelling with the Master Equation, chapter 0, pages 15-37, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60300-1_2
    DOI: 10.1007/978-3-319-60300-1_2
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