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3.7. Shift Factor in a Distribution

Applies to: @RISK 4.x–7.x

What is the shift factor of a distribution, and why it is used?

The shift factor of a distribution is shown in the RiskShift( ) property function. It moves the function toward the right on the x-axis (positive shift factor) or toward the left on the x-axis (negative shift factor). In other words, it shifts the domain of the distribution. This is equivalent to taking every point on the distribution and adding the shift factor to it, in the case of a positive shift. With a negative shift, that amount is subtracted from every point on the distribution.

Shift factor in defined distributions

When you're defining a distribution, click the down arrow next to "Parameters: Standard", and select Shift Factor on the pop-up dialog. The shift factor is now added to the Define Distributions dialog for this distribution, and you can enter various values and see how they change the distribution. If you don't want to have to do that, go into Utilities » Application Settings » Distribution Entry and change Shift Factor to Always Displayed.

You can always add a shift factor to an existing distribution by editing the Excel formula directly. For example, if you change =RiskLognorm(10,10) to RiskLognorm(10,10,RiskShift(3.7)), the entire distribution shifts 3.7 units to the right.

In general the shift factor should only be used in cases where the distribution function itself does not contain a location parameter. For example, you shouldn't use a shift factor for a normal distribution, since the mean of the normal is already a location parameter.

Shift factor in fitted distributions

In fitting distributions to data, the purpose of the shift factor is to allow fitting a particular distribution type because it has the right shape, even though the values in the fitted distribution might actually violate the defined parameter limits for that distribution.

For example, the 2-parameter log-normal distribution defined in @RISK cannot return negative numbers. But suppose your data have a log-normal shape but contain negative numbers. @RISK inserts a negative shift factor in the fitted distribution, thus shifting it from the usual position of a log-normal to the position that best approximates your data. In effect, this makes a 3-pararameter version of the log-normal distribution.

See also: Truncate and Shift in the Same Distribution

Additional keywords: log normal, Lognorm, RiskLognorm

Last edited: 2017-03-29

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