# Part 2: What are distributions?

### What is a distribution ?

The distribution of a variable is a description of the relative numbers of times each possible outcome will occur in a number of trials. The function describing the probability that a given value will occur is called the probability function (or probability density function, abbreviated PDF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

Continuous distributions – describe an infinite number of possible data values (blue line in the figure below).

Discrete distributions – describe a finite number of possible values (red bars in the figure below). ### What is a normal distribution ?

A normal distribution is a continuous distribution that is “bell-shaped” (blue line in above figure). The exact shape of the normal distribution (the characteristic of the „bell curve“) is defined by a function which has only two parameters: mean and standard deviation. In a normal distribution, data are most likely to be at the mean. Data are less likely to farther away from the mean. For example, ask yourself if people around you are more likely to be short, tall, or average in height?

To analyze a set of data, the most common approach is to assume that the data follow a certain distribution. The normal distribution is the most commonly used one as many statistical tests are based on the normal distribution such as t tests, ANOVA, linear and nonlinear regression. That is why the normal distribution is very important in statistic.

### Some Other distributions

• Binomial distribution

The binomial distribution measures the probabilities of the number of successes over a given number of trials with a specified probability of success in each try. A negative binomial distribution estimates the number of trials you will have before you reach the specified number of successes.

• Poisson distribution

The Poisson distribution measures the likelihood of a number of events occurring within a given time interval, where the key parameter is the average number of events in the given interval (l).

• Geometric distribution

Rather than focus on the number of successes in n trials, assume that you were measuring the likelihood of when the first success will occur.

• Hypergeometric distribution

The hypergeometric distribution measures the probability of a specified number of successes in n trials, without replacement, from a finite population.

• Discrete uniform distribution

This is the simplest of discrete distributions and applies when all of the outcomes have an equal probability of occurring.

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