Beginner tutorial · built-in distributions

Answer four questions with one distribution

A density describes local plausibility, a CDF answers “at most?”, a quantile finds a cutoff, and a random method simulates what could happen. JDistlib uses these four operations consistently.

The mental model

D, P, Q, and R

D · densityDensity for continuous data; exact probability mass for discrete data.
P · cumulativeThe probability that an observation is at or below a cutoff.
Q · quantileThe cutoff associated with a cumulative probability, such as the 95th percentile.
R · randomA simulated observation from the distribution, using a random stream.

In Java these are named density, cumulative, quantile, and random. They mirror R's d/p/q/r convention.

First code

A standard-normal probability and cutoff

Import the distribution class, then state the value, parameters, lower-tail choice, and whether the probability is logarithmic.

import jdistlib.Normal;

double probability = Normal.cumulative(
    1.96, 0.0, 1.0, true, false);
double cutoff = Normal.quantile(
    0.975, 0.0, 1.0, true, false);

// probability and cutoff are both about 0.975 and 1.96.

An instance remembers its parameters and is convenient when you reuse a law:

Normal measurement = new Normal(100.0, 15.0);
double below130 = measurement.cumulative(130.0, true, false);
double[] densities = measurement.density(
    new double[] {85.0, 100.0, 115.0});

Two switches

Lower tail and logarithmic probability

`lowerTail`

true asks for P(X ≤ x); false asks for P(X > x). Use the upper-tail calculation directly for rare exceedances.

`logP`

true returns the logarithm of a probability. This avoids underflow and is useful when likelihoods multiply many small probabilities.

double failureRisk = Normal.cumulative(
    180.0, 100.0, 15.0, false, false);
double logFailureRisk = Normal.cumulative(
    180.0, 100.0, 15.0, false, true);

Reproducible simulation

Own the random stream

Give each independent task its own RandomEngine. A fixed seed makes a tutorial, test, or analysis repeatable.

import jdistlib.Normal;
import jdistlib.rng.MersenneTwister;
import jdistlib.rng.RandomEngine;

RandomEngine random = new MersenneTwister(20260826L);
double[] simulated = Normal.random(
    1_000, 100.0, 15.0, random);

Do not share one mutable random engine between threads. Give each worker a separate, explicitly seeded stream.

Avoid surprises

Three common mistakes

Density is not interval probability

For a continuous law, use cumulative(b)-cumulative(a) for P(a < X ≤ b). A density value can exceed one.

Check the parameterization

Scale, rate, shape, and degrees of freedom are not interchangeable. Confirm them in the catalog.

Discrete density means mass

For a binomial or Poisson law, density(k,...) is the exact probability of k.

Estimate, then test carefully

A goodness-of-fit reference distribution should normally be fully specified. If parameters came from the same data, account for that estimation in the resampling procedure.

Scientific sources

Where the basic API comes from

Work through a complete analysis

Continue with the response-time vignette, browse the full catalog, search the probability citations, build a custom distribution, or learn how to adjust a collection of p-values in 0.7.0+.