stats

This README is the one indexed from the repository at its latest ref, not from the tag for this version.

# stats

An expressive implementation of statistical distributions.
Compatible with crystal v0.27.0.

## Installation

Add this to your application's `shard.yml`:

```yaml
dependencies:
  stats:
    github: Nephos/stats
```


## Usage

### Include it

```crystal
require "stats"
include Stats
```

### Normal distribution

```crystal
NormaleDistribution.between # less_than, greater_than
  standard_deviation: 15,
  esperance: 100,
  min: 85,
  max: 115
  # => 0.6826894921370859
```

### Binomial distribution

```crystal
Math.binomial_distribution(
  tries: 3,
  probability: 0.5,
  success: 1)
  # => 0.375
```

### Binomial coefficient

```crystal
Math.coef_binomial(5, 2) # => 10
```

### Factorial

```crystal
Math.factorial(4) # => 24
```

### Radian and degree

```crystal
90.radian # => (Math::PI / 2)
(Math::PI / 4) # => 45.0
```

### Series & Statistics

```crystal
[1, 2, 3].mean # => 2.0
[1, 2, 3].variance # => 0.6667
[1, 2, 3].standard_deviation # => 0.8165
[1, 2, 3].quadratic_mean # => 2.16
[2, 32].geometric_mean # => 8.0
[40, 60].harmonic_mean # => 48.0
[1,2,3,2,1].macd 3 # => [2.0, 2.333, 2.0]
```

### Correlations

```crystal
[1,2,3,4].covariance [4,2,1,0] # => -1.625
[1,2,3,4].correlation_coef [1,2,3,3] + 1 > 1.5 # => true
[1,2,3,4].correlation_coef [-14,14,101,-100] + 1 > 1.5 # => false
```

### Median

```crystal
[1, 2, 5].median # => 2.0
[42, 1337].median # => 685.5
```

### Quartiles & Boxplot

*Note: not big compatible yet*

```crystal
[1, 3, 5].first_quartile  # => 2.0 (alias of lower_quartile)
[1, 3, 5].second_quartile # => 3.0 (alias of median)
[1, 3, 5].third_quartile  # => 4.0 (alias of upper_quartile)
[1, 3, 5].quartiles       # => [2.0, 3.0, 4.0] ([Q1, Q2, Q3])
```

```crystal
arr = [-23, -5, 2, 5, 5, 6, 7, 8, 14, 15, 42, 1337]

arr.first_quartile  # => 3.5  (Q1)
arr.second_quartile # => 6.5  (Q2)
arr.third_quartile  # => 14.5 (Q3)
arr.interquartile_range # => 11.0 (alias of iqr) (IQR = Q3 - Q1)

# Tukey's fences with k = 1.5 (default parameter value)
arr.lower_fence # => -13.0 (Q1 - 1.5 * IQR)
arr.upper_fence # => 31    (Q3 + 1.5 * IQR)
arr.lower_outliers # => [-23]
arr.upper_outliers # => [42, 1337]

# Tukey's fences with k = 3 for "far out" outliers
arr.upper_fence(3)    # => 47.5 (Q3 + 3 * IQR)
arr.upper_outliers(3) # => [1337]
```

### Frequency

```crystal
[0, 1, 2, 3].frequency_of(0) # => 0.25 (amount of X in the population, by the size of the population)
[0, 0, 1, 2, 3].all_frequencies # => { 0 => 0.4, 1 => 0.2, 2 => 0.2, 3 => 0.2}
```

## Development

- The lib should take care of "big" numbers

## Contributing

1. Fork it ( https://github.com/Nephos/stats/fork )
2. Create your feature branch (git checkout -b my-new-feature)
3. Commit your changes (git commit -am 'Add some feature')
4. Push to the branch (git push origin my-new-feature)
5. Create a new Pull Request

## Contributors

- [Nephos](https://github.com/Nephos) Arthur Poulet - creator, maintainer