Answer four questions with one distribution

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

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