Abstract
Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.
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References
P Hall. On the rate of convergence of normal extrems, J Appl Probab, 1979, 16: 433–439.
D Kortschak, E Hashorva. Efficient simulation of tail probabilities for sums of log-elliptical risks, J Comput Appl Math, 2013, 247: 53–67.
MR Leadbetter, G Lindgren, H Rootzén. Extremes and Related Properties of Random Sequences and Processed, Springer Verlag, New York, 1983.
X Liao, ZX Peng. Convergence rates of limit distribution of maxima of lognormal samples, J Math Anal Appl, 2012, 395: 643–653.
X Liao, ZX Peng, S Nadarajah. Tail behavior and limit distribution of maximum of logarithmic general error distribution, Comm Statist Theory Methods, 2014a, 43: 5276–5289.
X Liao, ZX Peng, S Nadarajah. Tail properties and asymptotic expansions for the maximum of the logarithmic skew-normal distribution, J Appl Probab, 2013a, 50: 900–907.
X Liao, ZX Peng, S Nadarajah. Asymptotic expansions for moments of skew-normal extremes, Statist Probab Lett, 2013b, 83: 1321–1329.
X Liao, ZX Peng, S Nadarajah, XQ Wang. Rates of convergence of extremes from skew-normal samples, Statist Probab Lett, 2014b, 84: 40–47.
T Mikosch, AV Nagaev. Large deviations of heavy-tailed sums with applications in insurance, Extremes, 1998, 1: 81–110.
KA Nair. Asymptotic distribution and moments of normal extremes, Ann Probab, 1981, 9: 150–153.
DB Nelson. Conditional heteroskedasticity in asset returns: a new approach, Econometrica, 1991, 59: 347–370.
ZX Peng, S Nadarajah, FM Lin. Convergence rate of extremes for the general error distribution, J Appl Probab, 2010, 47: 668–679.
S I Resnick. Extreme Values, Regular Variation and Point Processes, Springer Verlag, New York, 1987.
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Supported by the National Natural Science Foundation of China (11171275), the Natural Science Foundation Project of CQ(cstc2012jjA00029) and the Doctoral Grant of University of Shanghai for Science and Technology (BSQD201608).
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Yang, G., Liao, X. & Peng, Zx. Distributional expansion of maximum from logarithmic general error distribution. Appl. Math. J. Chin. Univ. 31, 157–164 (2016). https://doi.org/10.1007/s11766-016-3275-5
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DOI: https://doi.org/10.1007/s11766-016-3275-5