Part 2. MM4XL Tools > 1. Strategic Tools > Risk Analyst > 2. Simulation Never heard of it > Distribution types

## Risk Analyst

### Distribution types

Probability distribution functions (Pdfs) can be discrete or continuous.
Pdfs of the first class can take only integer values, and are sometimes also called integer distributions. These Pdfs are used to estimate numbers relating to people, errors, conformity, and other variables that can only take an integer value such as 1, 2, 3, 1878, and so on. Continuous variables, as suggested by the name, can take any value within their range, including non-integers. Continuous Pdfs are used for modeling variables such as time, speed, sales, costs, profit, and so on.  Pdfs can be symmetrical or asymmetrical.
The left and right side (tails) of the symmetrical distribution below have the same area under the curve (blue region). This means that there is an equal probability of obtaining values either below the mean value of the distribution or above it. This is the typical case of events such as the gender of a new born or the size of a new market. The asymmetrical distribution below, on the other hand, is telling us that the distribution produces a lower portion of values below the mean and more values above the mean. This could be the case of a growing market.  Pdfs can be mono-modal, bi-modal or may have an undefined mode.
The picture below on the left shows a mono-modal distribution. If, for example, it refers to the number of client calls by day of the week, the pdf is telling us that the peak (modal value) occurs in the fourth class, on Thursday. Some processes, mainly operational, may peak at two points as shown in the picture on the right, and are said bi-modal. Finally, there are cases, mainly with continuous variables, when the distribution does not exhibit a mode (most frequent) value, and it is called a pdf with undefined mode.  Pdfs can be infinite or truncated, at one or both ends.
The picture below on the left shows an infinite distribution, such as a Normal one, where there is an infinitesimal probability of getting a very large value (infinite indeed) either above or below the mean. The other two charts refer to a truncated distribution. The one in the middle, for instance an Exponential pdf, is truncated at one side: it cannot take values below zero but it can expand to infinite on the positive side. The Triangular pdf on the right is truncated at both ends and allows only values ranging within the minimum and maximum value on the horizontal axis.   Price: 238.00
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