Monte Carlo Distributions

Nexxim Monte Carlo analysis supports three distributions from which random values are selected—uniform, Gaussian, and limit (min/max).

Uniform Distribution

A uniform distribution generates values within a range centered on a nominal value. All values within the range have equal likelihood of selection.

The range for a uniform distribution can be specified using absolute bounds or relative bounds.

• With an absolute bound, the range is the nominal value plus or minus the absolute bound. For example, if the nominal value is zero and the absolute bound is 2.5, the range of values is -2.5 to +2.5.
• With a relative bound, the range is the nominal value plus or minus the relative bound times the nominal value. For example, if the nominal value is 10 and the relative bound is 0.1, the range of values is 9 to 11. Note that a relative range cannot have a nominal value of zero.

Selection from a uniform distribution can be set up to do multiple selections and simulate with the value that has the highest absolute deviation from the nominal value. For example, suppose the nominal value is zero and the range is from -2.5 to +2.5. With a multiplier of 5, the Monte Carlo analyzer might select the five values -1.1, 2.2, 0.7, -2.4, and -0.6. The most extreme value, -2.4, would be used in the simulation and the other selections would be discarded. The resulting output distribution is somewhat bimodal. If no multiplier is specified, the default is one selection.

Gaussian Distribution

A Gaussian distribution generates values from plus infinity to minus infinity (-¥ to +¥) centered on the mean or nominal value. A value within the distribution has a probability of selection determined by the standard deviation.

The standard deviation for a Gaussian distribution is specified using an absolute spread or a relative spread that represents a specified number of standard deviations.

• With an absolute spread, the standard deviation is the absolute spread divided by the number of standard deviations it represents. For example, if the absolute spread is 2 and it represents 3 standard deviations, the standard deviation is 2/3 or 0.6666.
• With a relative spread, the standard deviation is the relative spread times the mean, divided by the number of standard deviations represented by the product. For example, if the mean is 10, the relative spread is 0.2 and the product represents 3 standard deviations, the standard deviation is (10´0.2)/3 or 0.6666. Note that a relative spread cannot have a mean of zero.

Selection from a Gaussian distribution can be set up to do multiple selections and simulate with the value that has the highest absolute deviation from the nominal value. For example, suppose the mean value is zero, the standard deviation is 1.0, and the range is from the range is -1.5 to +1.5. With a multiplier of 5, the Monte Carlo analyzer might select the five values -0.1, 1.2, 0.7, -0.4, and 0.6. The most extreme value, 1.2, would be used in the simulation and the other selections would be discarded. The resulting output values would tend to be somewhat bimodal. If no multiplier is specified, the default is one selection.

Limit or Min/Max Distribution

A limit or min/max distribution generates two values offset an absolute distance from the nominal value. The two values have equal likelihood of selection. The two values are:

• The nominal value plus the absolute offset.
• The nominal value minus the absolute offset.