# [SciPy-user] lognormal distribution

Stephen Walton stephen.walton at csun.edu
Mon Mar 7 14:04:58 CST 2005

```Robert Kern wrote:

> If it's univariate, and you can write out the pdf or cdf as a
> function, then I believe you can subclass scipy.stats.rv_continuous,
> and it's rvs() method will numerically invert the cdf to generate it's
> random numbers.

This is so cool!  I had a desire to generate values on (0,1) where
values near 0.5 were less probable than values at the endpoints.  Here's
the implementation:

#---------------begin------------------------------
import Numeric as Num
from scipy.stats.distributions import rv_continuous

#
# CDF for the sunspot generation function.  If we make it a subclass
# of rv_continuous we get sunspot.rvs for free :-)
#

class sunspot_gen(rv_continuous):
pmin=0.1
def _pdf(self,x):
pmax=(Num.pi-2*self.pmin)/(Num.pi-2)
return((pmax-self.pmin)*(1-Num.sin(Num.pi*x))+self.pmin)
def _cdf(self,x):
pmax=(Num.pi-2*self.pmin)/(Num.pi-2)
return -(cos(pi*x)*pmin-cos(pi*x)*pmax-pmax*x*pi-pmin+pmax)/pi
sunspot = sunspot_gen(a=0.,b=1.,name='sunspot', longname='A sunspot
subdivision',extradoc="""

Sunspot distribution

This distribution represents the probability of a subdivision of a sunspot
into two spots of size x and (1-x), where x is a value from sunspot.rvs(0).
The PDF has a high probability of x near 0 or 1 and a low probability of x
near 0.5.

""")
#-----------------end--------------------------------

My only question:  what should I replace the 'import Numeric as Num'
with if I want to be able to work within the framework of using either
Numeric or numarray?  'import numerix as Num' doesn't seem to work.

```

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