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Behavioral Mathematics for Game AI by Dave Mark

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Parabolic Distributions

We can create another common and useful distribution in a similar fashion to the linear distribution above. By inserting an exponent into the formula, thus making the formula a quadratic function such as we discussed in Chapter 10, we create one of the veritably plethoric varieties of parabolic distributions. The linear distributions have a subtle advantage of expression over the uniform distributions in that the probability value changes over the range. Similarly, a parabolic distribution is slightly more expressive than a linear distribution in that the rate of change in probability changes over the range (Figure 11.18 ...

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