Normal Distribution

This chapter covers the wide range of variations in normal distribution. Some of these are skew-normal distribution, power lognormal distribution, Gibrat distribution, logit-normal distribution, folded normal distribution, and Levy distribution. The q-Gaussian distribution is a member of the family of Tsallis distributions. Like the normal distribution it is symmetrical about the mean and hence its skewness is zero. It can, however, represent highly leptokurtic data. The chapter shows the effect of changing q, with the mean (μ) is fixed at 0 and β fixed at 1. It would appear that increasing q above 1 makes the curve flatter and therefore reduces kurtosis. The title generalised normal distribution or generalised Gaussian distribution is applied to various forms of the distribution. While each is developed from the normal distribution, by the addition of shape parameters, the way in which this is done is quite different.