Compute the PDF for a time series.

Description

The minimum and maximum of a time series are used to count the data
points in equally sized bins. The first bin begins at the minimum
data value and the last bin ends at the maximum data value. The
bin counts are normalized by the total number of points to produce
the probability density function. The cumulative distribution is
calculated and compared to the Gaussian distribution. The time series
used is

  input(t) = Gaussian*randomg()+Uniform*random()+Constant,

where Gaussian, Uniform, and Constant are specified constands,
randomg() generates Gaussian random numbers with mean = 0 and
standard deviation = 1, and random() generates uniformly distributed
random numbers between 0 and 1.

Upper Panel: A time series of Gaussianly distributed random numbers with mean=0, variance=4.
Middle Panel: The Probability Density Function for above time series.
Lower Panel: The Cumulative distributive function (CDF) for the above time series plotted as black circles.. CDF(x) equals the probability that the real-valued random variable X is less than or equal to x. The red line is the CDF for a Gaussian distribution.

Equations

None.

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.