Image Processing Reference
In-Depth Information
(a) (b)
(c) (d)
Fig. 7. Details of the normal distribution generated with numerical and interval traces:
(a) and (b) Central part of the distribution; (c) and (d) Tail of the distribution.
Therefore, this experiment has shown that signals with normal distributions maintain their
shape and statistical parameters in the interval-based simulations, but they require fewer
computations to obtain similar degrees of accuracy.
The second part of this section evaluates the variations of the statistical estimators when
interval samples of a specific width are used to compute the mean and variance of the
random signals in the simulations. Now, the sequence of steps is as follows:
1. Generate the traces of the random samples following the specified PDF, and assign the
width of the intervals.
2. Compute the mean and the variance of the trace.
3. Repeat steps 1 and 2 to reduce the variance of the parameters ( M times).
4. Group the means and variances of the computed traces, and obtain the estimation and
the variations of the statistical parameters.
5. Repeat the previous steps assigning other interval widths.
These steps allow the computation of the means and variances of the estimators, instead of
averaging the computed histograms. Step 2 computes the mean and variance of the signals
specified in step 1, and step 4 averages the results of the mean and variance of the estimators
(in this experiment M is high, to ensure the reliability of estimator statistics).
Figure 8 shows the evolution of the estimators of the mean and the variance as a function of
the lengths of the traces (500, 1000 and 5000 samples) and the widths of the intervals
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