Continuous and Discrete Probability Distributions

Notice that the Distribution Gallery shows whether the probability distributions are continuous or discrete.

Continuous probability distributions, such as the normal distribution, describe values over a range or scale and are shown as solid figures in the Distribution Gallery. Continuous distributions are actually mathematical abstractions because they assume the existence of every possible intermediate value between two numbers. That is, a continuous distribution assumes there is an infinite number of values between any two points in the distribution.

Discrete probability distributions describe distinct values, usually integers, with no intermediate values and are shown as a series of vertical columns, such as the binomial distribution at the bottom of Figure 77, Distribution Gallery Dialog. A discrete distribution, for example, may describe the number of heads in four flips of a coin as 0, 1, 2, 3, or 4.

However, in many situations, you can effectively use a continuous distribution to approximate a discrete distribution even though the continuous model does not necessarily describe the situation exactly.

In the dialogs for the discrete distributions, Crystal Ball displays the values of the variable on the horizontal axis and the associated probabilities on the vertical axis. For the continuous distributions, Crystal Ball does not display values on the vertical axis since, in this case, probability can only be associated with areas under the curve and not with single values.

Initially, the precision and format of the displayed numbers in the probability and frequency distributions come from the cell itself. To change the format, see Customizing Chart Axes and Axis Labels.

The following sections list continuous and discrete distributions available in Crystal Ball:

Note:

Custom distributions can be defined as continuous, discrete, or both. For more information, see Custom Distribution.