cause-effect 0.2.0

A library for cause-effect relationships.

Install it

You can install cause_effect via:

$ pip install cause_effect

Alternatively, you can install from the code repository directly:

$ pip install hg+http://bitbucket.org/hyllos/cause_effect

Core Functions

pareto(values)

Is a pareto distribution present for a list of numbers (ratio <= 1)?

mccauses(values)

Which causes have the highest concentration (rank * value)?

mceffects(values)

Which effects have the highest concentration?

separator(values)`

From which value (including) does the highest concentration begin?

causes(values, effects=0.8)

Determine causes for specified share of effects.

effects(values, causes=0.2)

Determine effects for specified share of causes.

Secondary Functions

ratio(values)

entropy divided by control_limit.

entropy(values)

Calculate entropy for values.

control_limit(count)

Calculate control entropy for count number of elements (length of values).

Tertiary Functions

make_causes(count)

Return list of causes that is cumulative percent of count number of elements.

make_effects(values)

Return list of effects that is cumulative percent of values.

make_concentration(values)

Return list of concentration for list of values that is rank * value.

sort_list(values)

Return sorted list of numbers.

Parameters

values is a list of numbers. effects and causes must be a number between 0 and 1 (including). count is the length of the list of values.

Use it

The function pareto tells you whether a pareto distribution is present for a list of numbers:

from pareto import pareto, mccauses, mceffects
pareto([789, 621, 109, 65, 45, 30, 27, 15, 12, 9])
True

Here, we have a pareto distribution present. That is a minority causes a majority of effects.

But which minority causes which majority?

mccauses([789, 621, 109, 65, 45, 30, 27, 15, 12, 9])
0.2
mceffects([789, 621, 109, 65, 45, 30, 27, 15, 12, 9])
0.818815331010453

20% of causes effect 82% of results.

But which values are that 20%?

separator([789, 621, 109, 65, 45, 30, 27, 15, 12, 9])
621

All values greater or equal than 621 are those 20% causing 82% of results.

That’s it.

Dig Deeper

How many causes are required for only 90% of effects?

from pareto import causes, effects
causes([789, 621, 109, 65, 45, 30, 27, 15, 12, 9], 0.9)
0.4

40%.

How many effects are behind only 10% of causes?

effects([789, 621, 109, 65, 45, 30, 27, 15, 12, 9], 0.1)
0.458

45.8%.

How does it work?

pareto calculates the entropy for a list of effects:

from pareto import entropy, control_limit, ratio
entropy([789, 621, 109, 65, 45, 30, 27, 15, 12, 9])
1.9593816735406657

It calculates the entropy for a control group of ten elements. That is the length of our list.

control_limit(10)
2.7709505944546686

It then checks entropy is less or equal than control_limit.

This can be simplified to:

values = [789, 621, 109, 65, 45, 30, 27, 15, 12, 9]
entropy(values) / control_limit(len(values)) <= 1

The left side of the comparison is done by ratio. So, if you want to find out how nearby or far off you are from a pareto distribution, do:

ratio([109, 65, 45, 30, 27, 15, 12, 9])
1.051

If we remove the first two effects, the control_limit will be exceeded by the values. So, we learn here that the pareto distribution disappears with the first two effects.

mccauses and mceffects return the respective share of the causes and effects where concentration (rank * value) is highest.

History

0.2.0 (2016-10-21)

• Add function separator().

• Streamline tests.

0.1.0 (2016-10-20)

• First release on PyPI.