Probability distributions
The ACC Carbon Tool is a stochastic visualisation tool. It uses probability distributions to simulate emissions, emission occurrences, and carbon prices, which are described on the emitter groups and carbon pricings help pages.
The distributions that are available for use fall into several groups.
Deterministic
This is not actually a probability distribution: the emissions, occurrence years or prices do not vary between simulations.
| Keyword | Distribution |
|---|---|
deterministic or none |
Deterministic |
Normal
These distributions are based on the normal distribution
| Keyword | Distribution |
|---|---|
normal or normalpct |
Normal distribution |
truncnormal or normal or normalpct |
Truncated normal distribution |
lognormal or lognormalpct |
Lognormal distribution |
Other
Various other distributions.
| Keyword | Distribution |
|---|---|
uniform |
Continuous uniform distribution |
triangle |
Triangular distribution |
trapezoidal |
Trapezoidal distribution |
Summary
The following table summarises availability and parameters:
| Deterministic | Normal | Truncated normal | Lognormal | Uniform | Triangular | Trapezoidal | |
|---|---|---|---|---|---|---|---|
| Sources? | 1, 2 | 1, 2 | 1, 2 | 3 | 3 | ||
| Occurrences? | see below | 1 | 1 | 1 | |||
| Prices? | 1 | 1 | 1 | ||||
| Distribution parameters? | |||||||
| Year data | amount | mean, sd | mean, sd | mean, sd | min, max | min, mode, max | min, max (see below) |
Notes:
- Truncated below at zero for
emitsources, prices and occurrences - Truncated above at zero for
sinksources - Cannot be used for
emitorsinksources
Descriptions
Each of these distributions is described below, including the distribution parameters they require and the information that is required for each year.
Description
The emissions or carbon prices are determined deterministically.
Keywords: deterministic or none
Distribution parameters
None.
Year data
- The (deterministic) level of emissions or carbon price.
Special notes
If a deterministic distribution is specified for occurrences, the occurrence parameters (if present) are ignored.
For emit sources, occurrences,
and carbon pricings the amount will be set to
zero if it is negative.
For sink sources the amount will
be set to zero if it is positive.
Emissions changes
The location of the distribution is the amount — ie, the level of emissions or carbon price. The spread of the distribution is zero.
Description
The emissions or carbon prices are determined using the normal distribution,
Keywords: normal or normalpct
Distribution parameters
None.
Year data
-
The mean and standard deviation. If the
normalpctkeyword is used, the standard deviation is specified as a proportion of the mean. Thenormalpctkeyword cannot be used for occurrences or in a carbon pricing.
Special notes
The normalpct keyword can be used only in
sources.
If the normal or normalpct keyword is used for
emit or
sink sources, occurrences or
in a carbon pricing, the truncated normal
distribution is used (see below).
Emissions changes
The location of the distribution is the mean. The spread of the distribution is the standard deviation.
Description
The emissions or carbon prices are determined using the truncated normal distribution. For
sink sources, the distribution is truncated above
at zero with no lower bound. For other sources,
occurrences, and carbon pricings the
distribution is truncated below at zero with no upper bound.
Keyword: truncnormal, normal or normalpct.
Distribution parameters
None.
Year data
- The mean and standard deviation.
Special notes
The truncated normal distribution is used for emit or
sink sources, occurrences
and prices if the normal or
normalpct keywords are specified.
For emit sources, occurrences,
and carbon pricings the mean will be set to
zero if it is negative.
For sink sources the mean will
be set to zero if it is positive.
Emissions changes
The location of the distribution is the mean. The spread of the distribution is the standard deviation. Note that this can produce counter-intuitive results if the mean is close to zero.
Description
The emissions or carbon prices are determined using the lognormal distribution.
Keyword: lognormal or lognormalpct
Distribution parameters
None.
Year data
-
The mean and standard deviation.
If the
lognormalpctkeyword is used, the standard deviation is specified as a proportion of the mean.
Special notes
The lognormal distribution cannot be used for occurrences or prices.
If the lognormal keyword is used for sink sources,
the mean must be negative and a reversed lognormal distribution
will be used (ie, the lognormal distribution reflected in the y axis). For other
sources, the mean must be positive. The mean must not be zero.
Emissions changes
The location of the distribution is the mean. The spread of the distribution is the standard deviation.
Description
The emissions or carbon prices are determined using the uniform distribution.
Keyword: uniform
Distribution parameters
None.
Special notes
For emit sources, occurrences,
and carbon pricings the minimum and
maximum will be set to zero if they are negative.
For sink sources the minimum and
maximum will be set to zero if they are positive.
Year data
- The minimum and maximum.
Emissions changes
The location of the distribution is the median. The spread of the distribution is the range — the difference between the minimum and maximum.
Description
The emissions are determined using the triangular distribution.
Keyword: triangle
Distribution parameters
None.
Special notes
The triangular distribution cannot be used for emit or
sink sources, occurrences,
or carbon pricings.
Year data
- The minimum, mode and maximum.
Emissions changes
The location of the distribution is the mode. The spread of the distribution is the range — the difference between the minimum and maximum.
Description
The emissions are determined using the trapezoidal distribution.
Keyword: trapezoidal
Distribution parameters
A single parameter representing the ratio of the triangular areas of the distribution to the rectangular area. The triangular areas are assumed to be symmetrical.
Special notes
The trapezoidal distribution cannot be used for emit or
sink sources, occurrences,
or carbon pricings.
Year data
- The two bending points of the distribution — the minimum and maximum of the rectangular area.
Emissions changes
The location of the distribution is the average of the two bending points. The spread of the distribution is the range — the difference between the maximum and minimum.