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Getting Started

This guide will help you get up and running with UniDist.jl quickly.

Installation

UniDist.jl can be installed using Julia's package manager:

using Pkg
Pkg.add("UniDist")

Or from the Julia REPL package mode (press ]):

pkg> add UniDist

Basic Usage

Creating Distributions

Distributions are created by calling their constructor with the appropriate parameters:

using UniDist

# Normal distribution with mean=0 and standard deviation=1
normal = Normal(0.0, 1.0)

# Exponential distribution with rate=2.0
exponential = Exponential(2.0)

# Binomial distribution with n=10 trials and p=0.5 probability
binomial = Binomial(10, 0.5)

# Beta distribution with shape parameters α=2 and β=5
beta = Beta(2.0, 5.0)

Computing Probabilities

Probability Density/Mass Function

Use pdf to compute the probability density (continuous) or probability mass (discrete):

# P(X = x) for discrete, f(x) for continuous
pdf(Normal(0, 1), 0.0)      # ≈ 0.3989
pdf(Binomial(10, 0.5), 5)   # ≈ 0.2461

Cumulative Distribution Function

Use cdf to compute P(X ≤ x):

cdf(Normal(0, 1), 1.96)     # ≈ 0.975
cdf(Exponential(1.0), 1.0)  # ≈ 0.6321

Quantile Function

Use quantile to find the value x such that P(X ≤ x) = p:

quantile(Normal(0, 1), 0.975)   # ≈ 1.96
quantile(Normal(0, 1), 0.5)     # = 0.0 (median)

Random Sampling

Generate random samples using the r function:

# Generate 1000 samples from a standard normal
samples = r(Normal(0, 1), 1000)

# Generate a single sample
single = r(Normal(0, 1))

Distribution Properties

d = Normal(5.0, 2.0)

mean(d)      # 5.0
var(d)       # 4.0
support(d)   # (-Inf, Inf)

R-Style Shortcuts

If you're familiar with R, you can use the shorthand functions:

dist = Normal(0, 1)

d(dist, 0.0)   # Same as pdf(dist, 0.0)
p(dist, 1.96)  # Same as cdf(dist, 1.96)
q(dist, 0.975) # Same as quantile(dist, 0.975)
r(dist, 100)   # Random samples

Working with Multiple Values

All functions support vectorized operations:

d = Normal(0, 1)

# Compute PDF at multiple points
pdf(d, [-2.0, -1.0, 0.0, 1.0, 2.0])

# Compute CDF at multiple points
cdf(d, [-1.96, 0.0, 1.96])

# Compute multiple quantiles
quantile(d, [0.025, 0.5, 0.975])

Next Steps