關於偏斜常態的尺度混合分佈之研究

A study of the scale mixture of skew normal distribution

林佑駿(Yu-Chun Lin)

指導教授 ： 蘇南誠

國立臺北大學/商學院/統計學系/碩士(2013年)

摘要

我們將介紹並探討一新的厚尾分佈族，其包含 Azzalini and Capitanio [Azzalini, A. and Capitanio, A., 2003, Distributions
generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J. Roy. Soc. Ser. B 65, 367-389.] 所建構的偏斜 t 分佈。
我們將給出新分佈之機率密度函數、累積分佈函數及動差函數的封閉式，這些封閉式可以讓我們很容易地算出機率、偏態係數、峰態係數等相關數值。
最後我們會以模擬數據及兩個實例說明此新分佈之彈性。

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 [Azzalini, A. and Capitanio, A., 2003, Distributions
generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. 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 which allows us to easily compute probabilities,
skewness, kurtosis and related measurements. Finally we illustrate the flexibility of this new distribution with simulated data and real data.

並列關鍵字

half-normal ； recurrence relations ； skew-normal ； skew-t ； moments

參考文獻

fied view on skewed distributions arising from selestions. Canadian J.

bution as the scale mixture of a skew exponential power distribution

5. Azzalini, A., 2005. The skew-normal distribution and related multi-

multivariate skew normal distribution. J. Roy. Soc. Ser. B 61, 579-

perturbation of symmetry with emphasis on a multivariate skew t -