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.

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