Appendix A: Some More Background
283
A.7 Skew Probability Distributions
An example of a skew probability distribution that Kapteyn studied, is the
so-called ‘log-normal’ distribution. This is similar to the well-known Gaussian
probability distribution, but now when plotted on a logarithmic horizontal
scale. An example of a log-normal distribution has been drawn on the left in
Fig. A.5. To the right the same distribution on a logarithmic scale on the x
axis, so that it becomes the normal Gaussian distribution. The color changes
with integer values of the ‘dispersion’ σ .
In normal distribution, the mode (the maximum or most common value),
the median (half larger and half smaller) and the regular average have the same
value (in the figure 10 2 or 100). At the log-normal, the average is 127.8, but
the mode is at 62.2 and the median at 100.
Kapteyn went on to study a general family of skewed distributions, of which
this is only one example. An extensive, technical discussion of Kapteyn’s work
in the field of statistics has been published an article by Ida H. Stamhuis and
Eugene Seneta [96], but see also [97].
Fig. A.5 On the left a log-normal probability distributions. On the right the same distribution but plotted on a logarithmic horizontal scale. After [97]
283
A.7 Skew Probability Distributions
An example of a skew probability distribution that Kapteyn studied, is the
so-called ‘log-normal’ distribution. This is similar to the well-known Gaussian
probability distribution, but now when plotted on a logarithmic horizontal
scale. An example of a log-normal distribution has been drawn on the left in
Fig. A.5. To the right the same distribution on a logarithmic scale on the x
axis, so that it becomes the normal Gaussian distribution. The color changes
with integer values of the ‘dispersion’ σ .
In normal distribution, the mode (the maximum or most common value),
the median (half larger and half smaller) and the regular average have the same
value (in the figure 10 2 or 100). At the log-normal, the average is 127.8, but
the mode is at 62.2 and the median at 100.
Kapteyn went on to study a general family of skewed distributions, of which
this is only one example. An extensive, technical discussion of Kapteyn’s work
in the field of statistics has been published an article by Ida H. Stamhuis and
Eugene Seneta [96], but see also [97].
Fig. A.5 On the left a log-normal probability distributions. On the right the same distribution but plotted on a logarithmic horizontal scale. After [97]