A Note on Improved Approximation of the Binomial Distribution by the Skew-Normal Distribution

Ching-Hui Chang Ching-Hui Chang is Associate Professor of Statistics, Department of Applied Statistics & Information Science, Ming Chuan University, Taoyuan County, Taiwan, ROC. Jyh-Jiuan Lin is Associate Professor of Statistics, Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Nabendu Pal is Professor of Statistics, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA 70504-1010. Miao-Chen Chiang is Research Assistant in the Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Email address for correspondence: . We would like to thank the editor, Professor PeterWestfall, and an anonymous associate editor for their comments and suggestions which greatly improved the presentation of this note.

Jyh-Jiuan Lin Ching-Hui Chang is Associate Professor of Statistics, Department of Applied Statistics & Information Science, Ming Chuan University, Taoyuan County, Taiwan, ROC. Jyh-Jiuan Lin is Associate Professor of Statistics, Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Nabendu Pal is Professor of Statistics, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA 70504-1010. Miao-Chen Chiang is Research Assistant in the Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Email address for correspondence: . We would like to thank the editor, Professor PeterWestfall, and an anonymous associate editor for their comments and suggestions which greatly improved the presentation of this note.

Nabendu Pal Ching-Hui Chang is Associate Professor of Statistics, Department of Applied Statistics & Information Science, Ming Chuan University, Taoyuan County, Taiwan, ROC. Jyh-Jiuan Lin is Associate Professor of Statistics, Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Nabendu Pal is Professor of Statistics, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA 70504-1010. Miao-Chen Chiang is Research Assistant in the Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Email address for correspondence: . We would like to thank the editor, Professor PeterWestfall, and an anonymous associate editor for their comments and suggestions which greatly improved the presentation of this note.

Miao-Chen Chiang Ching-Hui Chang is Associate Professor of Statistics, Department of Applied Statistics & Information Science, Ming Chuan University, Taoyuan County, Taiwan, ROC. Jyh-Jiuan Lin is Associate Professor of Statistics, Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Nabendu Pal is Professor of Statistics, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA 70504-1010. Miao-Chen Chiang is Research Assistant in the Department of Statistics, Tamkang University, Tamsui, Taiwan, ROC. Email address for correspondence: . We would like to thank the editor, Professor PeterWestfall, and an anonymous associate editor for their comments and suggestions which greatly improved the presentation of this note.

Abstract

It is a common practice to approximate a binomial distribution by a suitable normal distribution when n, the number of trials, is moderately large. But when p, the probability of success, is not close to 0.5, the binomial distribution can be heavily skewed, and hence the usual normal approximation may not be a good idea. In this note we show that the skew-normal distribution can provide a far better approximation due to its flexibility, and it can be used to approximate distributions other than the binomial one.

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A Note on Improved Approximation of the Binomial Distribution by the Skew-Normal Distribution

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