Randomly stopped models

Gillian Heller, Mikis Stasinopoulos, Robert Rigby

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

    Abstract

    We introduce a method for modelling a continuous response which is the sum of a random number of terms. Examples are total insurance claim sizes (the total of all claims on a policy in a year), or total amount spent by credit card holders in a sector in a month, where there may be multiple spending episodes. The distribution of the number of terms may be, in principle, any discrete distribution defined on the non-negative integers; and each term has a continuous, right-skewed distribution. The resulting marginal distribution of the total amount is a mixed discrete-continuous model, with a probability mass at zero and a continuous component. The model explicitly specifies log-linear models for the four parameters in the total amount distribution. It may be fitted to data using a package written in R. The method is illustrated on an Australian motor vehicle insurance data set.
    Original languageEnglish
    Title of host publicationProceedings of the 22nd International Workshop on Statistical Modelling
    EditorsJoan del Castillo, Anna Espinal, Pere Puig
    Place of PublicationBarcelona, Spain
    PublisherL'Institut d'Estadistica de Catalunya, IDESCAT
    Pages323-328
    Number of pages6
    ISBN (Print)9788469059432
    Publication statusPublished - 2007
    EventInternational Workshop on Statistical Modelling (22nd : 2007) - Barcelona, Spain
    Duration: 2 Jul 20076 Jul 2007

    Workshop

    WorkshopInternational Workshop on Statistical Modelling (22nd : 2007)
    CityBarcelona, Spain
    Period2/07/076/07/07

    Keywords

    • mixture distribution
    • mean and dispersion modelling
    • insurance claims
    • compound Poisson
    • discrete mixture

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