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# 11 Essential Distributions That Data Scientists Use 95% of the Time

### Most important distributions in data science.

Statistical models assume an underlying data generation process.

Based on the assumed data generation process, we can:

Formulate the maximum likelihood estimation (MLE) step.

Determine the maximum likelihood estimates.

As a result, the model performance becomes entirely dependent on:

Your understanding of the data generation process.

The distribution you chose to model data with, which, in turn, depends on how well you understand various distributions.

We also looked at this in a recent deep dive on generalized linear models, where the entire performance was reliant on the data generation process we assumed: Generalized Linear Models (GLMs): The Supercharged Linear Regression.

Thus, it is crucial to be aware of some of the most important distributions and the type of data they can model.

The visual below depicts the 11 most important distributions in data science:

Today, let’s understand them briefly and how they are used.

**Normal Distribution**The most widely used distribution in data science.

Characterized by a symmetric bell-shaped curve

It is parameterized by two parameters—mean and standard deviation.

Example: Height of individuals.

**Bernoulli Distribution**A discrete probability distribution that models the outcome of a binary event.

It is parameterized by one parameter—the probability of success.

Example: Modeling the outcome of a single coin flip.

**Binomial Distribution**It is Bernoulli distribution repeated multiple times.

A discrete probability distribution that represents the number of successes in a fixed number of independent Bernoulli trials.

It is parameterized by two parameters—the number of trials and the probability of success.

**Poisson Distribution**A discrete probability distribution that models the number of events occurring in a fixed interval of time or space.

It is parameterized by one parameter—lambda, the rate of occurrence.

Example: Analyzing the number of goals a team will score during a specific time period.

**Exponential Distribution**A continuous probability distribution that models the time between events occurring in a Poisson process.

It is parameterized by one parameter—lambda, the average rate of events.

Example: Analyzing the time between goals scored by a team.

**Gamma Distribution**It is a variation of the exponential distribution.

A continuous probability distribution that models the waiting time for a specified number of events in a Poisson process.

It is parameterized by two parameters—alpha (shape) and beta (rate).

Example: Analysing the time it would take for a team to score, say, three goals.

**Beta Distribution**It is used to model probabilities, thus, it is bounded between [0,1].

Differs from Binomial in this respect that in Binomial, probability is a parameter.

But in Beta, the probability is a random variable.

**Uniform Distribution**All outcomes within a given range are equally likely.

It can be continuous or discrete.

It is parameterized by two parameters: a (minimum value) and b (maximum value).

Example: Simulating the roll of a fair six-sided die, where each outcome (1, 2, 3, 4, 5, 6) has an equal probability.

**Log-Normal Distribution**A continuous probability distribution where the logarithm of the variable follows a normal distribution.

It is parameterized by two parameters—mean and standard deviation.

Example: Typically, in stock returns, the natural logarithm follows a normal distribution.

**Student t-distribution**It is similar to normal distribution but with longer tails.

It is used in t-SNE to model low-dimensional pairwise similarities. We covered it here: t-SNE article.

**Weibull**Models the waiting time for an event.

Often employed to analyze time-to-failure data.

👉 Over to you: Which important distributions have I missed here?

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## 11 Essential Distributions That Data Scientists Use 95% of the Time

Isn’t the binomial distribution just a special case of the Bernoulli distribution?