Probability distribution

Probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. This range will be between the minimum and maximum statistically possible values, but where the possible value is likely to be plotted on the probability distribution depends on a number of factors. These factors include the distribution's mean (average), standard deviation, skewness, and kurtosis.

Definition

In statistics, a probability distribution can be defined as a function that describes the likelihood of obtaining the possible values that a random variable can assume. In other words, the values of the variable correspond to the outcomes of a random phenomenon, and the probability of each value represents the frequency of the outcome when the phenomenon is performed a large number of times.

Types of Probability Distributions

There are many types of probability distributions in statistics including:

• Normal Distribution
• Binomial Distribution
• Poisson Distribution
• Exponential Distribution

Normal Distribution

The Normal Distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

Binomial Distribution

The Binomial Distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials with the same probability of success. The Bernoulli distribution is a special case of the binomial distribution where a single trial is conducted.

Poisson Distribution

The Poisson Distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

Exponential Distribution

The Exponential Distribution is the probability distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.

See Also

• Statistical Theory
• Statistical Analysis
• Probability Theory

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