On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient

Mogens Bladt, Bo Friis Nielsen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    In this article we use the concept of multivariate phase-type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation coefficient (also negative). Secondly, the class satisfies that any linear combination (projection) of the marginal random variables is a phase-type distribution. The latter property is partially important for the development of hypothesis testing in linear models. Finally, it is easy to simulate the exponential random vectors.
    Original languageEnglish
    JournalStochastic Models
    Volume26
    Issue number2
    Pages (from-to)295-308
    ISSN1532-6349
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Arbitrary correlation
    • Bivariate exponential distribution
    • Matrix-exponential
    • Phase-type distribution

    Cite this

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    title = "On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient",
    abstract = "In this article we use the concept of multivariate phase-type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation coefficient (also negative). Secondly, the class satisfies that any linear combination (projection) of the marginal random variables is a phase-type distribution. The latter property is partially important for the development of hypothesis testing in linear models. Finally, it is easy to simulate the exponential random vectors.",
    keywords = "Arbitrary correlation, Bivariate exponential distribution, Matrix-exponential, Phase-type distribution",
    author = "Mogens Bladt and Nielsen, {Bo Friis}",
    year = "2010",
    doi = "10.1080/15326341003756486",
    language = "English",
    volume = "26",
    pages = "295--308",
    journal = "Stochastic Models",
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    publisher = "Taylor & Francis Inc.",
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    On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient. / Bladt, Mogens; Nielsen, Bo Friis.

    In: Stochastic Models, Vol. 26, No. 2, 2010, p. 295-308.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient

    AU - Bladt, Mogens

    AU - Nielsen, Bo Friis

    PY - 2010

    Y1 - 2010

    N2 - In this article we use the concept of multivariate phase-type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation coefficient (also negative). Secondly, the class satisfies that any linear combination (projection) of the marginal random variables is a phase-type distribution. The latter property is partially important for the development of hypothesis testing in linear models. Finally, it is easy to simulate the exponential random vectors.

    AB - In this article we use the concept of multivariate phase-type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation coefficient (also negative). Secondly, the class satisfies that any linear combination (projection) of the marginal random variables is a phase-type distribution. The latter property is partially important for the development of hypothesis testing in linear models. Finally, it is easy to simulate the exponential random vectors.

    KW - Arbitrary correlation

    KW - Bivariate exponential distribution

    KW - Matrix-exponential

    KW - Phase-type distribution

    U2 - 10.1080/15326341003756486

    DO - 10.1080/15326341003756486

    M3 - Journal article

    VL - 26

    SP - 295

    EP - 308

    JO - Stochastic Models

    JF - Stochastic Models

    SN - 1532-6349

    IS - 2

    ER -