Distributions

Sample from the continuous uniform distribution U(low, high). Every value in [low, high) is equally likely. PDF: f(x) = 1/(high − low) for x ∈ [low, high). Mean = (low + high)/2, Variance = (high − low)²/12.

Sample from the normal (Gaussian) distribution N(μ, σ²). Uses the Box-Muller transform for generation. The bell curve — 68% of values fall within ±1σ of the mean, 95% within ±2σ, 99.7% within ±3σ.

Random floats uniformly distributed in [0, 1). Shorthand for uniform(0, 1, shape). The most basic random tensor — use it for random masks, dropout, and Monte Carlo sampling.

Random floats from the standard normal distribution N(0, 1). Shorthand for normal(0, 1, shape). Used for Gaussian noise injection, weight initialization (Xavier/He), and generative models.

Sample from the binomial distribution B(n, p). Each sample counts the number of successes in n independent Bernoulli trials, each with success probability p. PMF: P(k) = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ. Mean = np, Variance = np(1−p). When n=1, this is a Bernoulli distribution.

Sample from the Poisson distribution with rate λ. Models the number of events occurring in a fixed time interval when events happen independently at a constant average rate. PMF: P(k) = λᵏe⁻λ / k!. Mean = Variance = λ. Approximates B(n,p) when n is large and p is small.

Sample from the exponential distribution with rate λ. Models the waiting time until the next Poisson event. The only memoryless continuous distribution — P(X > s+t | X > s) = P(X > t). PDF: f(x) = λe⁻λˣ for x ≥ 0. Mean = 1/λ, Variance = 1/λ².

Sample from the gamma distribution Γ(α, β). Generalizes the exponential (α=1) and chi-squared (α=k/2, β=0.5) distributions. PDF: f(x) = βᵅ xᵅ⁻¹ e⁻βˣ / Γ(α) for x > 0. Mean = α/β, Variance = α/β². Used as a conjugate prior in Bayesian statistics.

Sample from the beta distribution Beta(α, β). Values are always in (0, 1), making it natural for modeling probabilities, proportions, and rates. PDF: f(x) = xᵅ⁻¹(1−x)ᵝ⁻¹ / B(α,β). Mean = α/(α+β). When α=β=1, this is uniform; when α=β>1, it is bell-shaped; when α≠β, it is skewed.

Random integers uniformly distributed in [low, high). Each integer in the range is equally likely with probability 1/(high − low). Output dtype is int32. Useful for random indexing, label generation, and discrete sampling.

Generate a random permutation. If x is a number n, returns a random permutation of [0, 1, ..., n−1]. If x is a 1D Tensor, returns a new tensor with elements shuffled in random order (does not mutate the input). Uses the Fisher-Yates algorithm for O(n) uniform shuffling.

Draw a random sample from a 1D tensor. With replace=true (default), the same element can appear multiple times (bootstrap sampling). With replace=false, elements are drawn without replacement (like dealing cards). Provide p for weighted sampling — p must sum to 1.

Shuffle elements of a tensor in place using the Fisher-Yates algorithm. This is the ONLY mutating operation in deepbox/ndarray — all other tensor operations return new tensors. O(n) time, O(1) extra space.