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  1. No Access

    Article

    Necessary conditions for characterization of laws via mixed sums

    SupposeX andY are independent and identically distributed, and independent ofU which satisfies 0≤U≤1. Recent work has centered on finding the lawsL(X) for whichX ℞U(X+Y) where ℞ denotes equality in law. We show t...

    Anthony G. Pakes in Annals of the Institute of Statistical Mathematics (1994)

  2. No Access

    Article

    Characterizations, length-biasing, and infinite divisibility

    SupposeL(X) is the law of a positive random variableX, andZ is positive and independent ofX. Admissible solution pairs (L(X),L(Z)) are sought for the in-law equation

    Anthony G. Pakes, T. Sapatinas, E. B. Fosam in Statistical Papers (1996)

  3. No Access

    Article

    Characterization of laws by balancing weighting against a binary operation

    LetL(X) be the law of a positive random variableX, andZ be positive and independent ofX. Solution pairs (L(X), L(Z)) are sought for the in-law equation ...

    Anthony G. Pakes in Statistical Papers (1996)

  4. No Access

    Article

    Extreme order statistics on Galton-Watson trees

    This paper studies the asymptotic behaviour of extreme order statistics of i.i.d. random scores ascribed to each individual in a Galton-Watson family tree. Of interest is the asymptotic behaviour of the order ...

    Anthony G. Pakes in Metrika (1998)

  5. No Access

    Article

    Criteria for Convergence of the Number of Near Maxima for Long Tails

    Let M n denote the maximum of a random sample of size n and K n (a) be the number of near maxima, i.e. the number of sample observations in the...

    Anthony G. Pakes in Extremes (2004)

  6. No Access

    Article

    Limit theorems for numbers of near-records

    Observations occurring between successive record times and within a distance a > 0 of the current record value are called near-records. Limit theorems for the number ξ n

    Anthony G. Pakes in Extremes (2007)

  7. No Access

    Article

    Some properties of the exponential distribution class with applications to risk theory

    This paper derives some equivalent conditions for tail equivalence of a distribution G and the convolution G*H, where G belongs to the exponential distribution class and H is another distribution. This generalize...

    Dongya Cheng, Fenglian Ni, Anthony G. Pakes… in Journal of the Korean Statistical Society (2012)

  8. No Access

    Article

    Limit theorems for record counts and times in the F α -scheme

    We determine the almost sure and central limiting behaviour of the number of records and record times for the F α -scheme. Elementary methods are used to obtain ...

    Paul Doukhan, Oleg I. Klesov, Anthony G. Pakes, Josef G. Steinebach in Extremes (2013)

  9. No Access

    Article

    On relative stability and weighted laws of large numbers

    Weighted laws of large numbers are established for components which are independent copies of a positive relatively stable law and the weights comprise a regularly varying sequence. The index of regular variat...

    André Adler, Anthony G. Pakes in Extremes (2017)

  10. Article

    Open Access

    Structural properties of generalised Planck distributions

    A family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is a randomly scaled gamma law; it arises as the equilibrium la...

    Anthony G. Pakes in Journal of Statistical Distributions and Applications (2021)

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