Modeling marked point processes via bivariate mixture transition distribution models

Mohamed Yusuf Hassan, Keh Shin Lii

    Research output: Contribution to journalReview articlepeer-review

    9 Citations (Scopus)


    We propose new probability models for the analysis of marked point processes. These models deal with the type of data that arrive or are observed in possibly unequal time intervals, such as financial transactions and earthquakes, among others. The models treat both the time between event arrivals and the observed marks as stochastic processes. We adopt a class of bivariate distributions to form the bivariate mixture transition distribution. In these models the conditional bivariate distribution of the next observation given the past is a mixture of conditional distributions given each one of the last p observations or a selection of past p events. The identifiability of the model is investigated, and an EM algorithm is developed to obtain estimates of the model parameters. Simulation and real data examples are used to demonstrate the utility of these models.

    Original languageEnglish
    Pages (from-to)1241-1252
    Number of pages12
    JournalJournal of the American Statistical Association
    Issue number475
    Publication statusPublished - Sept 2006


    • Bivariate distributions
    • Bivariate mixture transition distribution model
    • EM algorithm
    • Identifiability
    • Marked point processes

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty


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