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Monte Carlo Supported Distributions¶

The fourteen distributions Quantum XL builds in, with the parameter boxes each one shows. They are listed here in the order the dialog lists them.

This is the page the Help button opens on Mark Input, and it opens at the section for whichever distribution is selected at the time.

Continuous	Discrete
Normal	Uniform (Discrete)
Log-Normal	Poisson
Exponential	Binomial
Uniform	Binary
Triangular	Constant
Weibull
Gamma
Logistic
Log-Logistic

Two things the list also offers¶

Your own distributions. Any custom distribution or Empirical variable defined in the workbook is appended to this list, after the fourteen, under the name you gave it. Those have no parameter boxes: their data lives in the workbook. See Custom Distributions and Create Empirical.

Linked to a cell, the last entry, and offered by Mark Input alone. The distribution is then whatever a worksheet cell names, read at run time rather than chosen here.

The Mark Input dialog, the Distribution Gallery and the design sheet's in-cell dropdown are all shown the same list, so none of the three can offer a distribution the others do not.

Six distributions carry an Offset box: Exponential, Weibull, Gamma, Poisson, Binomial and Binary.

Offset shifts the whole distribution along the axis. It does not change the shape or the spread; it moves where the distribution starts. An Exponential with an offset of 5 produces values from 5 upwards instead of from 0 upwards. Leave it at 0 and you have the ordinary two-parameter form.

Normal Distribution¶

Parameter
Mean	the centre
Standard deviation	the spread

Symmetric, unbounded in both directions. The most common choice for a dimension or a measured property that varies about a target.

This is the one distribution whose boxes start filled in, at a Mean of 0 and a Standard deviation of 1, so a freshly marked cell shows a live preview straight away. Any saved marking replaces those.

Exponential Distribution¶

Parameter
Offset	where the distribution starts
Lambda	the rate

Bounded below by the offset and unbounded above, and always falling: the smallest values are the most likely. A larger Lambda means a faster fall and therefore a smaller mean, which is the opposite of what a scale parameter does.

Uniform Distribution¶

Parameter
Lower	the smallest value
Upper	the largest value

Every value between the two is equally likely, and nothing outside them occurs. The continuous one: it produces values with decimals. For whole numbers use Uniform (Discrete).

Triangular Distribution¶

Parameter
Minimum	the smallest value
Mode	the most likely value
Maximum	the largest value

Bounded at both ends, with a straight-line rise to the mode and a straight-line fall after it. The Mode does not have to sit midway, so the distribution can lean either way.

Log-Normal Distribution¶

Parameter
Mean (log)	the mean of the underlying normal
Standard deviation (log)	the standard deviation of the underlying normal

Bounded below by 0, unbounded above, and skewed right. Both parameters are in log units, which the labels say and which is the mistake this distribution invites: they are the mean and standard deviation of the logarithm of the variable, not of the variable.

Weibull Distribution¶

Parameter
Offset	where the distribution starts
Beta (shape)	the shape
Alpha (scale)	the scale

Bounded below by the offset and unbounded above. Its shape changes completely with Beta: at 1 it is the exponential, below 1 it falls away from the offset, and above 1 it rises to a peak and then falls, looking more symmetric as Beta grows.

Gamma Distribution¶

Parameter
Offset	where the distribution starts
Shape	the shape
Scale	the scale

Bounded below by the offset and unbounded above, and skewed right. Shape controls how far from symmetric it is and Scale stretches it without changing that.

Logistic Distribution¶

Parameter
Location	the centre
Scale	the spread

Symmetric and unbounded in both directions, like the normal, with more of its probability further from the centre.

Log-Logistic Distribution¶

Parameter
Location	the centre, in log units
Scale	the spread, in log units

Bounded below by 0, unbounded above, and skewed right. It stands to the logistic as the log-normal stands to the normal: both parameters describe the logarithm of the variable.

Uniform (Discrete) Distribution¶

Parameter
Lower	the smallest value
Upper	the largest value

Whole numbers only, every one from Lower to Upper equally likely. Both ends are included.

Poisson Distribution¶

Parameter
Offset	where the counts start
Mean	the average count

Whole numbers, bounded below by the offset and unbounded above. For a count of events in a fixed interval. Its mean and its variance are the same number, so choosing the mean has fixed the spread as well: it is not a parameter you can set separately here.

Binomial Distribution¶

Parameter
Offset	where the counts start
Number of trials	how many trials
Probability of success	the chance each one succeeds

Whole numbers from the offset to the offset plus the number of trials. The count of successes in a fixed number of independent trials.

Binary Distribution¶

Parameter
Offset	the value that stands for 0
Probability of 1	the chance of the higher of the two values

Two outcomes and nothing else, listed in the dialog as Binary (Bernoulli). With the offset at 0 it produces 0 and 1.

Constant Distribution¶

Parameter
Value	the value

One value, every trial. It does not vary, which is the point: mark an input Constant to hold it still while the rest of the model varies, without unmarking it and losing its settings.