Modelling Poisson marked point processes using bivariate mixture transition distributions

M. Y. Hassan, M. Y. El-Bassiouni

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)


    A class of bivariate continuous-discrete distributions is proposed to fit Poisson dynamic models in a single unified framework via bivariate mixture transition distributions (BMTDs). Potential advantages of this class over the current models include its ability to capture stretches, bursts and nonlinear patterns characterized by Internet network traffic, high-frequency financial data and many others. It models the inter-arrival times and the number of arrivals (marks) in a single unified model which benefits from the dependence structure of the data. The continuous marginal distributions of this class include as special cases the exponential, gamma, Weibull and Rayleigh distributions (for the inter-arrival times), whereas the discrete marginal distributions are geometric and negative binomial. The conditional distributions are Poisson and Erlang. Maximum-likelihood estimation is discussed and parameter estimates are obtained using an expectation-maximization algorithm, while the standard errors are estimated using the missing information principle. It is shown via real data examples that the proposed BMTD models appear to capture data features better than other competing models.

    Original languageEnglish
    Pages (from-to)1440-1452
    Number of pages13
    JournalJournal of Statistical Computation and Simulation
    Issue number8
    Publication statusPublished - Aug 2013


    • EM algorithm
    • Internet traffic
    • Poisson time series models
    • continuous-discrete bivariate distribution models
    • high-frequency financial data
    • identifiability
    • marked point processes
    • negative binomial models
    • observation-driven models

    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation
    • Statistics, Probability and Uncertainty
    • Applied Mathematics


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