View source for Tutorial:JMathLab/Statistics (Descriptive)


= Descriptive Statistics =

jMathLab is well suited for statistical calculations. You can calculate the major statistical characteristics
for matrices and vectors. Let us calculate '''mean, variance and standard deviations''' for a vector:

<jc lang="math">
v=[1,10,20,2,4,7,4,3]
a=mean(v); printf('%f\n',a)
a=var(v); printf('%f\n',a)
a=std(v); printf('%f\n',a)
</jc>

Similarly, you can do this for matrices:

<jc lang="math">
v=[1,10,20,2,4,7,4,3; 6,1,2,20,42,7,41,3;]
a=mean(v); printf('%f\n',a)
a=var(v); printf('%f\n',a)
a=std(v); printf('%f\n',a)
</jc>

= Correlations =

You can also calculate correlations between two vectors or two matrices.
For example, calculate '''covariance and coefficient of correlations''' as:

<jc lang="math">
v1=[1,10,20,2,4,7,4,3]
v2=[3,11,10,3,5,5,7,3]
a=cov(v1,v2);           printf('Covariance=%f\n',a)
a=correlation(v1,v2);   printf('Coeff. correlation=%f\n',a)
</jc>

Analogously, you can do similar calculations for matrices.

= Probability distributions =

jMathlab supports custom tailored numerical integration of certain probability distributions.
Look at the package '''statistics_probability''' in [http://jwork.org/jmathlab/doc/| jMathLab reference].
As example, '''normal_prob'''   returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to x. The argument can be either a number or vector. In the latter case, one can plot such integrals for any sequence of numbers.

Here is an example:

<jc lang="math">
a=-0.001:0.0001:0
y=normal_prob(a)
plot2d()
draw2d(a,y) % draw areas under the normal distribution for a vector
</jc>


= Histograms =

One can fill histograms with data from vectors and matricies.

<jc lang="math">
y=poisson_rnd(2,100)
h=h1d('Poisson',20,1,10,y) 
plot2d()
draw2d(h)
</jc>

Here we create a vector with random numbers distributed using the  Poisson statistics.
Then we create a histogram with the title "Poisson", 20 bins, in the range between 1 and 10.
Then we use '''draw2d()''' to display the histogram. You can access the descriptive statistics as
for any vector or matrix.

= Random numbers =
You can create vectors and matrices with random numbers using the major distributions.
Look at the package [http:/jwork.org//jmathlab/doc/ random_numbers] for the description of various random-number generators.

For example, let us create a vector and a matrix with the random numbers distributed
in accordance with a Poisson distribution (assuming the mean 2):

<jc lang="math">
v=poisson_rnd(2,10)   % create vector with 10 elements 
m=poisson_rnd(2,10,3) % create matrix 10x3
printf('%f',m)        % print
</jc>