October 2017
Intermediate to advanced
624 pages
17h 24m
English
A generalised form of the logistic distribution is described by

Depending on the sign of δ, the distribution is either lower‐bounded or upper‐bounded.
The CDF is
The CDF can be inverted

Figure 22.1 shows the effect of changing δ with α fixed at 0 and β at 1. Note that all the curves pass through the point (α, 0.25β). Fitting Equation (22.4) to the C4 in propane data gives α as 2.30, β as 1.27 and δ as 0.360. RSS is 0.0529, m\aking the distribution a relative poor choice.
Figure 22.1 Logistic: Effect of δ on shape
The mean and variance are

As δ → 0, from Equation (11.4), we obtain the density functions ...