gdstats

gdstats currently provides a small set of common distributions all implemented in fast forms usually via inversion techniques:

Discrete (integers)

• randi_bernoulli(p), return 1 or 0 based on probability p

  example: Whether a specific die value was rolled or not

• randi_binomial(p, n), return the number of 1s on n many Bernoulli Trials probability p.

  example: Number of times a specific value is rolled on a die in n many trials

• randi_geometric(p), return the number of Bernoulli Trials with probability p until a result of 1.

  example: The number of rolls on a die until a specific value shows.

• randi_poisson(lambda), a binomial where p->0 and n->inf but n*p = lambda.

  example: Number of phone calls in a given amount of time. p is very low and n is very large.

• randv_histogram(values, probabilities), provide a list of return values and probabilities and return a value fitting the distribution.

  example: Use for distributions of own choosing such as marbles in a bag.

• randi_pseudo(c), mimics the Warcraft3/Dota style of "fair" number generators. Gives the number of actions until an event occurs where upon a failure, the probability increases by c.

  example: Use to determine the number of attacks until the next critical occurs.

Table of Nominal Probabilities to c Values

The following table gives values of c to approximate a given event's probability of occuring.

Nominal Probability	c	Nominal Probability	c
5%	0.00380	45%	0.20155
10%	0.01475	50%	0.24931
15%	0.03222	55%	0.36040
20%	0.05570	60%	0.42265
25%	0.08474	65%	0.48113
30%	0.11895	70%	0.57143
40%	0.15798

Continuous (floats)

• randf_uniform(a, b), return a uniformly random value in range a to b

  example: Same as rand_range

• randf_exponential(lambda), return a value fitting the exponential distribution

  example: Time between independant events which occur at a constant average rate. Memoryless

• randf_erlang(k, lambda), Sum of k many exponentials of 1/lambda.

  example: The distribution of time between k many incoming telephone calls modelled by a poisson process. k = 1 is the exponential.

• randf_gaussian()/randf_normal(), return a value from the normal distribution.

  example: Useful in modeling realistic scenarious which use the distribution, i.e. Harmonic Oscilator ground state, position of a diffused particle.