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  • 1. Gut, Allan
    et al.
    Martin-Löf, Anders
    Stockholm University, Faculty of Science, Department of Mathematics.
    Extreme-trimmed St. Petersburg games2015In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 96, p. 341-345Article in journal (Refereed)
    Abstract [en]

    Let S-n, n >= 1, describe the successive sums of the payoffs in the classical St. Petersburg game. Feller's famous weak law, Feller (1945), states that s(n)/n log(2) n (sic) 1 as n -> infinity. However, almost sure convergence fails, more precisely, lim supn ->infinity S-n/n log(2) n = +infinity a.s. and lim inf(n ->infinity) S-n/n log(2) n = 1 a.s. as n -> infinity. Csorgo and Simons (1996) have shown that almost sure convergence holds for trimmed sums, that is, for S-n - max(1 <= k <= n) X-k and, moreover, that this remains true if the sums are trimmed by an arbitrary fixed number of maximal sums. A predecessor of the present paper was devoted to sums trimmed by the random number of maximal summands. The present paper concerns analogs for the random number of summands equal to the minimum, as well as analogs for joint trimmings.

  • 2.
    Hao, Chengcheng
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Liang, Yuli
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Roy, Anuradha
    Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data2015In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 106, p. 113-120Article in journal (Refereed)
    Abstract [en]

    Centers and vertices principal component analyses are common methods to explain variations within multivariate interval data. We introduce multivariate equicorrelated structures to vertices’ covariance. Assuming the structure, we show equivalence between centers and vertices methods by proving their eigensystems proportional.

  • 3.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    A note on the connection between some classical mortality laws and proportional frailty2017In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 126, p. 76-82Article in journal (Refereed)
    Abstract [en]

    We provide a simple frailty argument that produces the Gompertz-Makeham mortality law as the population hazard rate under the assumption of proportional frailty given a common exponential hazard rate. Further, based on a slight generalisation of the result for the Gompertz-Makeham law the connection to Perks and Beard's mortality laws is discussed. Moreover, we give conditions for which functional forms of the baseline hazard that will yield proper frailty distributions given we want to retrieve a certain overall population hazard within the proportional frailty framework.

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