Genesis of the Lognormal Distribution
Life is log-normal! Science and art, life and
statistics (by E. Limpert and
dvi (=device indepentent) or
the applet illustrating the lognormal version of the "Galton Board".
The program is mostly self-explaining. When you start it, you see
the triangle configuration for the lognormal distribution and some
default parameters. The simulation is not yet running. You can now
customize the model by switching to the normal distribution
(Galton board) or by changing the default parameters to your own
values. The important model parameters are:
You can also change the size of the balls, and you can move their
entry point using the scrollbar. The dynamic behaviour of the model
can be influenced by changing speed and frequency: The ball
speed is not an exact quantity and therefore has no units. It
corresponds approximately to the number of pixels (=unities) per
0.01 seconds. The ball frequency is the number of newly entered
balls per second. Depending on the choice of some parameters, some
other parameters have to be adjusted. To start the simulation,
press the start-button. The stop-button allows you to
interrupt the simulation: The current balls will move on to their end
position, but no new balls will be entered. The start-stop cycle can be
repeated. The simulation ends when the first bucket is full: Then the
screen is frozen and current balls will not move on to their end
position. Before, during and after the simulation, the curve of
the corresponding distribution function can be displayed. Before the
simulation, the curve is equal to the x-axis. The parameters cannot be
changed during and after the simulation. To start a new simulation with
new parameters, press the reset-button.
- The lognormal-factor (or the increment in case of normal
distribution), defining the relation of the horizontal
position of the tips of triangles in two neighbour
- The number of triangle rows.
- AITCHISON, J., BROWN, J.A.C., The lognormal distribution,
Cambridge University Press, Cambridge, 1957.
- CROW, E.L., SHIMIZU, K., (Eds.), Lognormal Distributions:
Theory and Application, Dekker, New York, 1988.
- GALTON, F., Natural Inheritance, Macmillan, London, 1889.
- LIMPERT, E., ABBT, M., STAHEL W.A., Lognormal distributions
across the sciences - keys and clues, 1998, submitted.
- MCALISTER D., Proc. Roy. Soc. 29 (1879),
- WILRICH, P.-T., et al., Formeln und Tabellen der
angewandten mathematischen Statistik, 3. Aufl., Springer,
Berlin, 1987, p.37f.
About this page
The page and specially the model were developped by Christian Gut as
a Semesterarbeit at the
Institute of Scientific Computing of the
, supervised by
Dr. Hans Hinterberger and
Dr. Eckhard Limpert.
The page follows some ideas of the
Leitprogramm by Prof. Dr. Karl Frey.