Uniform convergence rates of skew-normal extremes

• Autorzy: Xiong Qian , Peng Zuoxiang , Nadarajah Saralees

Identyfikatory

DOI

10.37190/0208-4147.00129

• Języki publikacji: EN

Abstrakty

EN

Let Mn = max(X1, . . . , Xn) denote the partial maximum of an independent and identically distributed skew-normal random sequence. In this paper, the rate of uniform convergence of skew-normal extremes is derived. It is shown that with optimal normalizing constants the convergence rate of [formula] to its ultimate extreme value distribution is proportional to [formula].

Słowa kluczowe

EN

extreme value distribution; rate of uniform convergence; skew-normal distribution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2023
• Tom: Vol. 43, Fasc. 2
• Strony: 165 --184

Twórcy

autor

Xiong Qian

• School of Mathematics and Statistics, Southwest University, 400715 Chongqing, P.R. China

autor

Peng Zuoxiang

• School of Mathematics and Statistics, Southwest University, 400715 Chongqing, P.R. China

autor

Nadarajah Saralees

• Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Bibliografia

• A. A. Azzalini (1985), A class of distributions which includes the normal ones, Scand. J. Statistics 12, 171-178.
• B. B. Carmichael and A. Co¨en (2013), Asset pricing with skewed-normal return, Finance Res. Lett. 10, 50-57.
• 1. S. Chang and M. G. Genton (2007), Extreme value distributions for the skew-symmetric family of distributions, Comm. Statist. Theory Methods 36, 1705-1717.
• 2. N. Counsell, M. Cortina-Borja, A. Lehtonen and A. Stein (2011), Modelling psychiatric measures using skew-normal distributions, Eur. Psychiatry 26, 112-114.
• 3. A. Gasull, M. Jolis and F. Utzet (2015a), On the norming constants for normal maxima, J. Math. Anal. Appl. 422, 376-396.
• 4. A. Gasull, J. A. L´opez-Salcedoand and F. Utzet (2015b), Maxima of gamma random variables and other Weibull-like distributions and the Lambert W function, Test 24, 714-733.
• 5. M. G. Genton (2004), Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, Chapman and Hall/CRC, Boca Raton.
• 6. P. Hall (1979), On the rate of convergence of normal extremes, J. Appl. Probab. 16, 433-439.
• 7. F. Hosseini, J. Eidsvik and M. Mohammadzadeh (2011), Approximate Bayesian inference in spatial glmm with skew normal latent variables, Comput. Statist. Data Anal. 55, 1791-1806.
• 8. H. Kim M. and B. K. Mallick (2004), A Bayesian prediction using the skew Gaussian distribution, J. Statist. Planning Inference 120, 85-101.
• 9. M. R. Leadbetter, G. Lindgren and H. Rootz´en (1983), Extremes and Related Properties of Random Sequences and Processes, Springer, New York.
• 10. X. Liao and Z. Peng (2012), Convergence rates of limit distribution of maxima of lognormal samples, J. Math. Anal. Appl. 395, 643-653.
• 11. X. Liao, Z. Peng and S. Nadarajah (2013a), Asymptotic expansions for moments of skew-normal extremes, Statist. Probab. Lett. 83, 1321-1329.
• 12. X. Liao, Z. Peng and S. Nadarajah (2013b), Tail properties and asymptotic expansions for the maximum of logarithmic skew-normal distribution, J. Appl. Probab. 50, 900-907.
• 13. X. Liao, Z. Peng and S. Nadarajah (2014a), Tail behavior and limit distribution of maximum of logarithmic general error distribution, Comm. Statist. Theory Methods 43, 5276-5289.
• 14. X. Liao, Z. Peng, S. Nadarajah and X. Wang (2014b), Rates of convergence of extremes from skew normal samples, Statist. Probab. Lett. 84, 40-47.
• 15. K. A. Nair (1981), Asymptotic distribution and moments of normal extremes, Ann. Probab. 9, 150-153.
• 16. Z. Peng, S. Nadarajah and F. Lin (2010), Convergence rate of extremes for the general error distribution, J. Appl. Probab. 47, 668-679.
• 17. R. Vasudeva, K. J. Vasantha and S. Ravi (2014), On the asymptotic behaviour of extremes and near maxima of random observations from the general error distributions, J. Appl. Probab. 51, 528-541.
• 18. Q. Xiong and Z. Peng (2020), Asymptotic expansions of powered skew-normal extremes, Statist. Probab. Lett. 158, art. 108667, 10 pp.
• 19. C. Zeller, C. Cabral and V. Lachos (2016), Robust mixture regression modeling based on scale mixtures of skew-normal distributions, Test 25, 375-396.