Python Programming for Biology: Bioinformatics and Beyond

Geometric distribution

For  an  event  of  specified  probability,  the  geometric  distribution  is  the  probability

distribution for the number of independent trials that do not  result  in  the  event,  until  the

event is observed once. If we consider the event a ‘success’, then the distribution is over

the  number  of  ‘failures’.  A  good  example  of  this  is  the  distribution  of  DNA  fragment

lengths  after  being  cut  with  an  enzyme  like  HindIII.  Here  the  event  is  a  cut  site  and  the

distribution of the number of other DNA positions we observe before finding a cut site is

geometric. For the geometric distribution the probability of a number of independent non-

event trials (k) required to observe the event with stated probability (p) is given by:

Pr(k) = (1 − p)

k − 1

p

Here k takes integer values from one. A different formula arises if k starts at zero, i.e. Pr(k)

= (1−p)

k

p, which represents the number of trials required before the event occurs, i.e. not

including the event. As it happens, the scipy.stats.geom function uses the first form, which

includes  the  event.  The  geometric  distribution  is  related  to  a  more  general  distribution

called the negative binomial distribution that represents the probability distribution for the

number of trials that occur before an arbitrary number of events of stated probability occur

(rather than just one).

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