OpenOffice Calc Tips

The lognormal distribution is defined with reference to the normal distribution. A random variable is lognormally distributed if the logarithm of the random variable is normally distributed.

The lognormal distribution is commonly used for general reliability analysis, cycles-to-failure in fatigue, material strengths and loading variables in probabilistic design. Another advantage of the lognormal distribution is that it is positive-definite, so it is often useful for representing quantities that cannot have negative values. Lognormal distributions have proven useful as distributions for rainfall amounts, for the size distributions of aerosol particles or droplets, and for many other cases.

The following formula can be used to generate lognormal random data

=LOGINV(RAND(),meanlog,sdlog)

This is illustrated in the example sheet below…

The formula in C6 is =LOGINV(RAND();$C$2;$C$3). Drag and fill for the rest of the table.

Just to convince ourselves that we have lognormally distributed data, we take each value in the lognormally distributed data set and calculate the natural log - below.

Here, the formula in cell H6 is =LN(C6) Drag and fill as before.

The frequency distribution table & corresponding chart for our lognormally distributed data.

For the corresponding normally distributed data, we see anaverage of 1.972 and standard deviation of 1.05 - which is expected - given our initial parameters for the lognormally distributed data.

This entry was posted on Monday, October 3rd, 2005 at 3:05 pm and is filed under Math & Statistics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.