I made a Markov chain chatbot for IRC in Python a few years back and can shed some light how I did it. The text generated does not necessarily make any sense, but it can be really fun to read. Lets break it down in steps. Assuming you have a fixed input, a text file, … Read more
Generate a uniformly distributed random number. Iterate through your list until the cumulative probability of the visited elements is greater than the random number Sample code: double p = Math.random(); double cumulativeProbability = 0.0; for (Item item : items) { cumulativeProbability += item.probability(); if (p <= cumulativeProbability) { return item; } }
If the sampling is with replacement, you can use this algorithm (implemented here in Python): import random items = [(10, “low”), (100, “mid”), (890, “large”)] def weighted_sample(items, n): total = float(sum(w for w, v in items)) i = 0 w, v = items[0] while n: x = total * (1 – random.random() ** (1.0 / … Read more
There’s one in scipy.stats: >>> import scipy.stats >>> scipy.stats.norm(0, 1) <scipy.stats.distributions.rv_frozen object at 0x928352c> >>> scipy.stats.norm(0, 1).pdf(0) 0.3989422804014327 >>> scipy.stats.norm(0, 1).cdf(0) 0.5 >>> scipy.stats.norm(100, 12) <scipy.stats.distributions.rv_frozen object at 0x928352c> >>> scipy.stats.norm(100, 12).pdf(98) 0.032786643008494994 >>> scipy.stats.norm(100, 12).cdf(98) 0.43381616738909634 >>> scipy.stats.norm(100, 12).cdf(100) 0.5 [One thing to beware of — just a tip — is that the parameter … Read more
Yes, you can. Since GUIDs are 128 bits long, there is admittedly a minute possibility of a clash—but the word “minute” is nowhere near strong enough. There are so many GUIDs that if you generate several trillion of them randomly, you’re still more likely to get hit by a meteorite than to have even one … Read more
Because nextDouble works like this: (source) public double nextDouble() { return (((long) next(26) << 27) + next(27)) / (double) (1L << 53); } next(x) makes x random bits. Now why does this matter? Because about half the numbers generated by the first part (before the division) are less than 1L << 52, and therefore their … Read more
You are looking for the alias method which provides a O(1) method for generating a fixed discrete probability distribution (assuming you can access entries in an array of length n in constant time) with a one-time O(n) set-up. You can find it documented in chapter 3 (PDF) of “Non-Uniform Random Variate Generation” by Luc Devroye. … Read more
xor is a dangerous default function to use when hashing. It is better than and and or, but that doesn’t say much. xor is symmetric, so the order of the elements is lost. So “bad” will hash combine the same as “dab”. xor maps pairwise identical values to zero, and you should avoid mapping “common” … Read more
As far as I see, the problem is (as you already wrote), that MeanResidualLife takes a long time to compute, even for a single evaluation. Now, the FindMinimum or similar functions try to find a minimum to the function. Finding a minimum requires either to set the first derivative of the function zero and solve … Read more
How to generate a random point within a circle of radius R: r = R * sqrt(random()) theta = random() * 2 * PI (Assuming random() gives a value between 0 and 1 uniformly) If you want to convert this to Cartesian coordinates, you can do x = centerX + r * cos(theta) y = … Read more