Updatable discrete probability distribution
This module provides functionality for working with discrete probability distributions. A discrete probability distribution (DPD) represents the probability distribution of a discrete random variable, where each possible value (category) has an associated probability weight.
The DPD in this module supports operations such as initialization, updating category weights, sampling categories according to their probabilities, and calculating the total weight of the distribution.
The DPD module is designed to be used in various applications that involve discrete probability distributions, such as stochastic simulations, Markov chain Monte Carlo (MCMC) methods, and probabilistic modeling.
Example usage:
let dpd = Discrete_pd.init 3 ~f:(fun i -> float (i + 1))
Discrete_pd.update dpd 1 4.0
let rng = Gsl.Rng.(make (default ()))
let category = Discrete_pd.draw dpd rngIn the example above, a discrete probability distribution (dpd) with 3 categories is initialized, and the weight of category 1 is updated. Then, a category index is sampled using the DPD and a random number generator (rng).
val init : int -> f:(int -> float) -> tinit n ~f initializes an updatable discrete probability distribution with n categories. It takes a function f that specifies the weight for each category.
Example:
let dpd = init 3 ~f:(fun i -> float (i + 1))This initializes a discrete probability distribution with 3 categories and assigns weights 1.0, 2.0, and 3.0 to each category respectively.
val update : t -> int -> float -> unitupdate dpd i w_i updates the weight of category i in the discrete probability distribution dpd to the new weight w_i.
Example:
let dpd = init 3 ~f:(fun i -> float (i + 1))
update dpd 1 4.0This updates the weight of category 1 in the discrete probability distribution dpd to 4.0.
val draw : t -> Gsl.Rng.t -> intdraw dpd rng samples a category index from the discrete probability distribution dpd using the random number generator rng. It returns the index of the sampled category.
Example:
let dpd = init 3 ~f:(fun i -> float (i + 1))
let rng = Gsl.Rng.(make (default ()))
let category = draw dpd rngval total_weight : t -> floattotal_weight dpd returns the total weight of all categories in the discrete probability distribution dpd.
Example:
let dpd = init 3 ~f:(fun i -> float (i + 1))
let weight = total_weight dpdThis calculates the total weight of all categories in the discrete probability distribution dpd and assigns it to the variable weight.
demo ~n ~ncat is a demo function that generates a discrete probability distribution with ncat categories and generates a sample of size n from it. It returns a tuple formed by the probability distribution and the frequencies in the sample.
Example:
let probabilities, counts = demo ~n:1000 ~ncat:5This generates random probabilities, creates an updatable discrete probability distribution with 5 categories, performs 1000 sampling trials, and assigns the generated probabilities normalized by their sum to the variable probabilities and the counts of each sampled category divided by 1000 to the variable counts.