Overview for Probability Distributions

The probability density function (PDF) is an equation that represents the probability distribution of a continuous random variable. The PDF curve indicates regions of higher and lower probabilities for values of the random variable. For example, for a normal distribution, the highest PDF value is at the mean, and lower PDF values are in the tails of the distribution.

For a discrete distribution, such as a binomial distribution, you can use the PDF to determine the probability of exact data values (also called the Probability Mass Function or PMF).

For more information, go to Using the probability density function (PDF).

The cumulative distribution function (CDF) calculates the cumulative probability for a given x-value. Use the CDF to determine the probability that a random observation that is taken from the population is less than or equal to a certain value. You can also use this information to determine the probability that an observation is greater than a certain value, or between two values. For example, a cumulative distribution function can show the proportion of trees in a forest that have diameter measurements of 10 inches or less.

For more information, go to Using the cumulative distribution function (CDF).

The inverse cumulative distribution function (ICDF) gives the value of the variable that is associated with a specific cumulative probability. For example, a reliability engineer wants to determine the time by which specific proportions of components fail. The engineer can use the ICDF to determine the 95^th percentile of the failure time distribution.

For more information, go to Using the inverse cumulative distribution function (ICDF).