# [SciPy-User] Confusion about lognormal distribution functions

josef.pktd@gmai... josef.pktd@gmai...
Sun Nov 27 11:49:24 CST 2011

```On Sun, Nov 27, 2011 at 12:39 PM, Robert Kern <robert.kern@gmail.com> wrote:
> On Sat, Nov 26, 2011 at 16:52, tazz_ben <tazz_ben@wsu.edu> wrote:
>> Hi Group -
>>
>> So, what I'm trying to do is draw a firm size from a lognormal
>> distribution in a simulation (I'm using a fortuna RNG outside of the scope
>> of this question -- why instead of twister deals with my research
>> question, for this purposes it is just important to say using the built in
>> random draw from a specific distribution wouldn't work).
>>
>> But when I do something like this:
>>
>> from scipy.stats import lognorm
>>
>> lognorm.ppf(.5,1,50,50)
>>
>> The numbers that come out make no sense (I'm right in believing "loc" =
>> "mean" and "scale" = "standard deviation"?). I've tried logging the
>> numbers, un-logging the numbers, etc.  I'm very confused on what it is
>> doing.
>
> No, loc and scale mean exactly the same thing for every distribution.
> loc translates the distribution linearly and scale scales it.
>
>  lognorm.pdf(x, s, loc=loc, scale=scale) == lognorm.pdf((x-loc)/scale, s)/scale
>
> They don't always map to particular parameters in standard
> parameterizations. However, they often do, so doing this lets us share
> the code for shifting and scaling in the base class rather than
> implementing it slightly differently for every distribution.
>
> In this case, you want to ignore the loc parameter entirely. The scale
> parameter corresponds to exp(mu) where mu is the mean of the
> underlying normal distribution. The shape parameter is the standard
> deviation of the underlying normal distribution.
>
> log(lognorm.ppf(p, s, scale=scale)) == norm.ppf(p, loc=log(scale), scale=s)

just as background http://projects.scipy.org/scipy/ticket/1502 and

It's a FAQ. It might be a case for writing a reparameterized wrapper class.

Josef

>
> --
> Robert Kern
>
> "I have come to believe that the whole world is an enigma, a harmless
> enigma that is made terrible by our own mad attempt to interpret it as
> though it had an underlying truth."
>   -- Umberto Eco
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```