Python Programming for Biology: Bioinformatics and Beyond

Figure 21.9.  An example output of the Poisson distribution. A graph of the output

generated using the poisson.pmf() function from the scipy.stats module, tested for an event

rate of 2500. The graph illustrates the probability density for discrete numbers of events in

the range from 2300 to 2700. This is a very good approximation for the binomial

distribution illustrated above (

Figure 21.7

).

Figure 21.10.  An example output of the geometric distribution. A graph of the output

generated using the geom.pmf() function from the scipy.stats module, tested for an event

probability of 0.0025. The graph illustrates the probability for the number of independent

trials until the event occurs, in the range from 0 to 1000.

Again we can use SciPy to calculate the probabilities for the distribution, here using the

probability  for  a  restriction  enzyme  cut  site  to  get  the  distribution  in  the  DNA  fragment

lengths:

from scipy.stats import geom

from numpy import array

p = 0.0025

geomRandomVar = geom(p)

lengths = array(range(1, 1000))

probs = geomRandomVar.pmf(lengths)

pyplot.plot(lengths, probs)

pyplot.show()

The geometric distribution is the last discrete probability distribution we will describe

in  detail  but  there  are  several  other  distributions  that  are  easily  accessible  in  Python  via

---

their  implementation  in  the  scipy.stats  module.  Some  of  the  more  notable  available

probability distributions are as follows:

dlaplace: the discrete Laplace distribution; the differences between two independent

but  identically  distributed  random  variables  which  themselves  have  geometric

distributions.

hypergeom:  the  hypergeometric  distribution,  describing  the  number  of  successful

events occurring after selecting a given number of items from a population without

replacement. (With replacement the distribution would be binomial.)

nbinom:  the  negative  binomial  distribution,  a  generalisation  of  the  geometric

distribution for a variable number of events.

randint: the uniform distribution, i.e. where all values are equally likely.

skellam: the Skellam distribution, the differences between two independent random

variables which themselves have Poisson distributions and different mean values.