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PMF operations and utilities

Source: R/PMF.R
PMF.Rd

A set of functions for working with Probability Mass Functions (PMFs) in bayesRecon. A PMF is represented as a normalized numeric vector where element v[j+1] represents the probability of value j (support starts from 0).

These functions provide utilities for:

  • Drawing samples from PMFs

  • Computing summary statistics (mean, variance, quantiles)

  • Summarizing PMF distributions

Usage

PMF_sample(pmf, N_samples)
PMF_get_mean(pmf)
PMF_get_var(pmf)
PMF_get_quantile(pmf, p)
PMF_summary(pmf, Ltoll = .TOLL, Rtoll = .RTOLL)

PMF_get_mean(pmf)

PMF_get_var(pmf)

PMF_get_quantile(pmf, p)

PMF_summary(pmf, Ltoll = .TOLL, Rtoll = .RTOLL)

Arguments

pmf

A PMF object (numeric vector where element j+1 is the probability of value j).

N_samples

Number of samples to draw from the PMF.

p

Probability level for quantile computation (between 0 and 1).

Ltoll

Lower tolerance for computing the minimum of the PMF (default: 1e-15).

Rtoll

Upper tolerance for computing the maximum of the PMF (default: 1e-9).

Functions

PMF_sample(pmf, N_samples)

Draws random samples from the probability distribution specified by the PMF. Uses sampling with replacement from the discrete support values, weighted by their probabilities. This is useful for generating synthetic data or for Monte Carlo simulations.

PMF_get_mean(pmf)

Computes the expected value (mean) of the distribution represented by the PMF. The mean is calculated as the sum of each value in the support weighted by its probability: \(\sum_{x} x \cdot P(X=x)\).

PMF_get_var(pmf)

Computes the variance of the distribution represented by the PMF. The variance measures the spread of the distribution and is calculated as \(E[X^2] - (E[X])^2\), where \(E[X]\) is the mean.

PMF_get_quantile(pmf, p)

Computes the quantile of the distribution at probability level p. Returns the smallest value x such that the cumulative probability up to x is greater than or equal to p. For example, p=0.5 gives the median.

PMF_summary(pmf, Ltoll, Rtoll)

Provides a comprehensive summary of the distribution including minimum, maximum, quartiles, median, and mean. The minimum and maximum are determined based on probability thresholds to handle the potentially infinite tails of discrete distributions.

Examples

library(bayesRecon)

# Let's build the pmf of a Binomial distribution with parameters n and p
n <- 10
p <- 0.6
pmf_binomial <- apply(matrix(seq(0, n)), MARGIN = 1, FUN = \(x) dbinom(x, size = n, prob = p))

# Draw samples from the PMF object
set.seed(1)
samples <- PMF_sample(pmf = pmf_binomial, N_samples = 1e4)

# Compute statistics
PMF_get_mean(pmf_binomial) # Mean: should be close to n*p = 6
#>      [,1]
#> [1,]    6
PMF_get_var(pmf_binomial) # Variance: should be close to n*p*(1-p) = 2.4
#>      [,1]
#> [1,]  2.4
PMF_get_quantile(pmf_binomial, 0.5) # Median
#> [1] 6
PMF_summary(pmf_binomial) # Full summary
#>   Min. 1st Qu. Median Mean 3rd Qu. Max
#> 1    0       5      6    6       7  10