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Some Results on the Non-Homogeneous Hofmann Process

In: Applied Probability Theory - New Perspectives, Recent Advances and Trends

Author

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  • Jose Alfredo Jimenez Moscoso
  • Gerson Yahir Palomino Velandia

Abstract

The classical counting processes (Poisson and negative binomial) are the most traditional discrete counting processes (DCPs); however, these are based on a set of rigid assumptions. We consider a non-homogeneous counting process (which we name non-homogeneous Hofmann process - NHP) that can generate the classical counting processes (CCPs) as special cases, and also allows modeling counting processes for event history data, which usually exhibit under- or over-dispersion. We present some results of this process that will allow us to use it in other areas and establish both the probability mass function (pmf) and the cumulative distribution function (cdf) using transition intensities. This counting process (CP) will allow other researchers to work on modelling the CP, where data dispersion exists in an efficient and more flexible way.

Suggested Citation

  • Jose Alfredo Jimenez Moscoso & Gerson Yahir Palomino Velandia, 2023. "Some Results on the Non-Homogeneous Hofmann Process," Chapters, in: Abdo Abou Jaoude (ed.), Applied Probability Theory - New Perspectives, Recent Advances and Trends, IntechOpen.
    • Handle: RePEc:ito:pchaps:287361
    DOI: 10.5772/intechopen.106422
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    More about this item

    Keywords

    mixed Poisson Process; Hofmann process; variance-to-mean ratio; transition intensity;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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