Why Do Distributions Matter in Modelling?

Because not all uncertainty looks the same.

Probabilistic models rely on distributions to simulate the uncertainty we see in real life. They help us:

• Predict likely outcomes, rather than just one “best guess”

• Estimate risks and costs

• Capture randomness, which is crucial in the drilling field where anything can happen but can also expand to Finance, Logistics, and AI.

Distributions are the engine of any probabilistic model. The better they reflect reality, the more useful your model becomes.

Real-World Use Cases

• Weather Forecasting: “There’s a 60% chance of rain” is based on probabilistic models trained on historical data and patterns.

• Recommendation Systems: Predicting which movie you might like next uses probability distributions to model user preferences.

• Medical Diagnosis: Algorithms estimate the probability of a condition based on symptoms and test results.

• Robotics and AI: Probabilistic models help machines deal with uncertain environments, like self-driving cars estimating where pedestrians might go.

Common Distributions:

• Normal Distribution (Gaussian)

The famous bell curve. It describes many natural phenomena — from IQ scores to errors in measurement. It’s symmetric, with most data clustering around the mean and fewer cases in the tails.

• Binomial Distribution

Used for binary outcomes — success/failure, win/lose. It answers: “What’s the probability of X successes in N trials?”

• Poisson Distribution

Ideal for counting events over time or space. Think: “How many cars pass through this checkpoint per hour?”

• Uniform Distribution

Every outcome is equally likely. Great for modelling total randomness, like rolling a fair die.

• Triangular Distribution

Simple model requiring a minimum, most likely, and maximum estimate, good for preliminary estimates of a new drilling operation where data is scarce.

• Pert Distribution

Similar to Triangular in that they are used for uncertain estimates. However, PERT has a smoothing effect by assuming most values cluster closer to the most likely estimate rather than being spread evenly. Parameters include three-point estimates: best-case estimate, most likely expected estimate, and worst-case estimate.

Final Thoughts

Understanding probabilistic distributions isn’t just about math. It is about thinking in terms of likelihoods, embracing uncertainty, and making smarter decisions.

PLANS turns uncertainty into strategy. With distributions, you're not just estimating—you’re outsmarting the competition.