A10.9 DISCRETE UNIFORM DISTRIBUTION

The discrete uniform is the discrete alternative of the Uniform distribution described above. The Discrete uniform distribution is defined by the following parameters:

• Lower bound X_min of the distribution;
• Upper bound X_max of the distribution;
• Step S (e.g. channel spacing in the case of frequency distributions);
• Step shift Ss (e.g. to set the step values to the centre frequency of the channel).

Figure 409: Discrete uniform distribution: parameters (left) CDF (right)

As a result, the generated discrete random parameter will be taking the following values:

                    (Eq. 145)

each value being assigned the same probability:

                                              (Eq. 146)

with i=1...N

     (Eq. 147)

The following examples, with a step shift of 0 and a step of 0.2, returns frequencies that will operate at 1000 MHz, for another snapshot it will be 1000.2 MHz, etc… the maximum value will be 1001 MHz

Figure 410: Discrete Uniform (with step 0)

Adding a step shift of 0.1 and keeping a step of 0.2, returns frequencies that will operate at 1000.1 MHz, 1000.3 MHz etc… with a maximum value of 1000.9 MHz.

Figure 411: Discrete Uniform (with step 0.1)