新廣義偏斜t分佈：性質與應用

A New Generalized Skew-t Distribution: Properties and Applications

林佑駿(You-Jiun Lin) ； 蘇南誠(Nan-Cheng Su)

《中國統計學報》 58卷1期 (2020/03) Pp. 45-69

摘要

我們將介紹並探討一新的厚尾分佈族，其包含Azzalini and Capitanio [Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution, 2003, J. Roy. Soc. Ser. B 65, 367-389]所建構的偏斜t分佈。我們將導出此新分佈之機率密度函數、累積分佈函數及各階動差的封閉式。這些封閉式有助於相關機率、偏態、峰態等數值的計算。最後，我們會以模擬數據及一個實例說明此分佈之實用性。

關鍵字

半常態分佈 ； 遞迴式 ； 偏斜常態分佈 ； 偏斜t分佈 ； 動差

並列摘要

A new class of heavy-tailed distribution, which contains Azzalini and Capitanio's skew-t distribution [Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution, 2003, J. Roy. Soc. Ser. B 65, 367-389 ] as a special case, is introduced and investigated. The probability density function, distribution function and moments of this new distribution are derived as a closed expression, which makes the related probabilities, skewness, kurtosis and related measurements easy to compute. Finally we illustrate the flexibility of this new distribution with various simulated data and real data.

並列關鍵字

Half-normal ； Recurrence relations ； Skew-normal ； Skew-t ； Moments

參考文獻

Arellano-Valle, R. B. and Azzalini, A. (2006). On the unification of families of skew-normal distributions. Scandinavian Journal of Statistics, 33(3): 561-574.

Arellano-Valle, R. B., Branco, M. D. and Genton, M. G. (2006). A unified view on skewed distributions arising from selections. Canadian Journal of Statistics, 34(4): 581-601.

Arslan, O. and Genc, A. I. (2009). The skew generalized t distribution as the scale mixture of a skew exponential power distribution and its applications in robust estimation. Statistics, 43(5): 481-498.

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12: 171-178.

Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica, 46(2): 199-208.