Python Programming for Biology: Bioinformatics and Beyond

2

The examples in this chapter were tested with SciPy 0.7.1.

3

http://www.r-project.org/

4

http://rpy.sourceforge.net/

5

If the distribution is a large data set which we know in its entirety the true mean may be

referred to as the population mean.

6

Cauchy

probability

density

function:

,

see

http://en.wikipedia.org/wiki/Cauchy_distribution

.

7

http://en.wikipedia.org/wiki/Bias_of_an_estimator

.

8

‘Delta degrees of freedom’.

9

The more extreme values can either be smaller or larger than the observation, depending

on the context.

10

 So  the  total  probability,  1  =

∫f(x)dx  where  the  integral  is  over  the  region  where  X  is

defined.  The  mean,  μ  =  E(X)  =

∫x f(x)dx  and  the  variance  is  still  E(X

2

)  −  E(X

2

),  where

E(X

2

) =

∫x

2

f(x)dx.

11

 Here  f(x)  can  be  thought  of  as  the  probability  that  the  random  variable  X  takes  the

value x, although that is not quite correct mathematically, since in general the probability

that X takes any precise value is 0, given there are an infinity of real numbers in a given

range. More correctly, f(x) is the probability that X takes values in the range (x−δ, x), then

divided by δ, and in the limit that δ approaches 0.