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.
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.
The mean, variance, skewness and kurtosis are
Figure 20.2 plots ...