Probability

### Methods

#### aggregate

Aggregates two probability estimates from independent sources about the occurrence of
a **single** event **a**. It returns the aggregated probability of occurrence
of the event **a**. The assumption here is that the two probabilities
(estimates) are not correlated with each other and the **common prior**
probability of **a** is **0.5**.

For a detailed explanation, refer to the paper titled
*Bayesian Group Belief by Franz Dietrich*
published in Social Choice and Welfare October 2010, Volume 35, Issue 4, pp 595–626.

##### Example

```
aggregate( 0.5, 0.6 );
// returns 0.6
aggregate( 0.5, 0.4 );
// returns 0.4
aggregate( 0.6, 0.6 );
// returns 0.6923076923076923
aggregate( 0.4, 0.6 );
// returns 0.5
```

##### Parameters

Name | Type | Description |
---|---|---|

pa1 | number | first estimate of probability of occurrence of event |

pa2 | number | second estimate of probability of occurrence of event |

##### Returns

the aggregated probability.

- Type
- number

#### range4CI

Computes probability from the **observed** count of successes (`successCount`

) out of the total count (`totalCount`

)
along with its **range** for required level of Confidence Interval (CI) i.e. `zscore`

.
The range is the minimum and maximum probability values for given `zscore`

or CI.

These computations are based on approach specified in the Wilson's *Notes on
Probable Inference, The Law of Succession, and Statistical Inference*
published in ASA's Journal.

For quick reference, typical value of `zscore`

for 90% and 95% CI is approximately
1.645 and 1.960 respectively.

##### Example

```
range4CI( 1, 10 );
// returns {
// probability: 0.18518871952479238,
// min: 0.02263232984000629,
// max: 0.34774510920957846
// }
range4CI( 10, 100 );
// returns {
// probability: 0.1105389143431459,
// min: 0.06071598345043355,
// max: 0.16036184523585828
// }
```

##### Parameters

Name | Type | Attributes | Default | Description |
---|---|---|---|---|

successCount | number | observed count of successes out of |
||

totalCount | number | the total count. |
||

zscore | number |
<optional> |
1.645 | for the required level of CI. |

##### Returns

containing `probability`

, `min`

and `max`

.

- Type
- object