Statistical Examples illustrated extracting some statistical properties of random patterns using descriptive statistics VIs. It also mentioned that the histogram is an indication of the probability density function.
The probability distribution function F(x) is defined as
where f(x) is the probability density function, and the following conditions on the probability density function have been imposed:
and
It follows from calculus theorems that
To obtain the probability density and distribution functions of the white noise pattern generator VIs, you can use the Histogram VI because it is a denormalized discrete representation of the probability density function. The discrete representation is
and the sum of the elements of the histogram is of the form
where m is the number of samples in the histogram, and n is the number of samples in the input sequence representing the function.
Thus, to obtain an estimate of the probability distribution function, it is only necessary to normalize the histogram by
factor and letting hj = xj
The following illustration shows a set of front panel controls with the block diagram below them. The VI uses 25,000 samples, 2,500 in each of 10 loop iterations, to generate the probability distribution function. The output array of the Integral x(t) VI is the probability distribution function. The differentiation of the distribution is the probability density function.
The following graph shows the last block of Gaussian-distributed noise samples.
The following graphs show the results of executing the previous block diagram. Notice that the curve corresponding to the probability distribution function is monotonically increasing and is limited to the maximum value of 1.00 as the value of the X axis increases.
Also notice that the probability density function shows a Gaussian distribution that conforms to the specific pattern selected when the VI generated the noise signal.