Custom Distribution

Notes

Custom Distribution, Exercise 0.6

He briefly mentions Lévy flights.

const r = p.random();

if (r < 0.01) {
  // 1% of the time take a large step
} else {
  // small step
}

Accept-Reject Algorithm

Numbers that have an easier time qualifying will be picked more often, and numbers that rarely qualify will be picked infrequently.

while (true) {
  // the number that you're checking
  const r1 = p.random(1);

  // assign a probability
  const probability = r1;

  // a qualifying random value that decides whether to keep the number
  const r2 = p.random(1);

  if (r2 < probability) {
    return r1;
  }
}

Exercise from the book:

Can you map the probability to a quadratic function by making the likelihood that a value is picked equal to the value squared?

He gives and example of a uniform distribution of random step sizes and says to change it:

const step = 10;
const stepx = random(-step, step);
const stepy = random(-step, step);
this.x += stepx;
this.y += stepy;