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2 results

  • ON THE CUMULATIVE DISTRIBUTION FUNCTION OF THE VARIANCE-GAMMA DISTRIBUTION

  • Part of
  • ROBERT E. GAUNT
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 110 / Issue 2 / October 2024
    Published online by Cambridge University Press:
    29 January 2024, pp. 389-397
    Print publication:
    October 2024
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  • We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From these formulas, we deduce exact formulas for the cumulative distribution function of the product of two correlated zero-mean normal random variables.

  • A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE

  • Part of
  • ROBERT STEWART, HONG ZHANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 87 / Issue 1 / February 2013
    Published online by Cambridge University Press:
    07 June 2012, pp. 115-119
    Print publication:
    February 2013
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  • Given a rectangle containing uniformly distributed random points, how far are the points from the rectangle’s centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided.