20Normal Distribution
In Chapter 5 we covered the classic normal distribution along with its bivariate version. Chapter 12 addressed the lognormal distribution – one of the common variations. Here we cover the wide range of other variations, many of which better fit our examples.
20.1 Skew‐Normal
As its name suggests the skew‐normal distribution is a modified form of the normal distribution that can take account of skewness. It is described by the PDF
The parameter δ determines skewness. Figure 20.1 shows its effect, with α set to 0 and β to 1. If δ is less than zero the distribution is skewed to the left, if greater than zero it is skewed to the right. If set to −1 or +1 we obtain the half‐normal distribution that we will describe later.
Figure 20.1 Skew‐normal: Effect of δ on shape
The mean, variance, skewness and kurtosis are
Figure 20.2 plots ...
Get Statistics for Process Control Engineers now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
