Lognormal Random Numbers Centered around a high value

Question

I am trying to create random numbers from a lognormal distribution using numpy/scipy.

The mean is given as 2000 and sigma as 800.

If I create my random valus using numpy.random.lognormal(mean=2000, sigma=800, size=10000) all I get is very high or inf numbers.

Is there a way to work around this?

score 6 · Accepted Answer · answered Oct 17 '12 at 15:42

6

Be careful: the mean and sigma arguments correspond to the distribution of the log of the lognormal distribution; the actual arithmetic mean of the distribution is exp(mean + sigma**2/2), which evaluates to inf in standard double precision floating point when mean=2000 and sigma=800.

See http://docs.scipy.org/doc/numpy/reference/generated/numpy.random.lognormal.html#numpy.random.lognormal and http://en.wikipedia.org/wiki/Log-normal_distribution for more details.

answered Oct 17 '12 at 15:42

Warren Weckesser

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is there an easy way to transform my mean and sigma to the needed values? – Lukas Mosser Oct 17 '12 at 15:50
the logmean of the distribution is known, but I need the mean of the underlying normal distribution. – Lukas Mosser Oct 17 '12 at 16:22
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The wikipedia article has the conversions (http://en.wikipedia.org/wiki/Log-normal_distribution#Arithmetic_moments). See also: www.stanford.edu/~bkravitz/research/lognormal.pdf (equations (3) - (6) give the conversions). – Warren Weckesser Oct 17 '12 at 16:40
@LukasMosser use `numpy.random.lognormal(mean=np.log(2000),sigma=np.log(800),size=10000)`...or maybe it's `np.log10`. Can't remember the math – Paul H Oct 17 '12 at 20:52
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@Paul H: No, it is not that simple. Read the link that I gave for the formulas. – Warren Weckesser Oct 17 '12 at 21:02
Maybe there should be a function that does this for us? :| – endolith Dec 07 '18 at 05:05

Lognormal Random Numbers Centered around a high value

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