# statistical utilities

Many of the files in this directory are a direct port of the functions from the [jerzy](https://github.com/pieterprovoost/jerzy) package to contemporary TypeScript.

## Features

- [Distributions](#distributions)
- [One- and two-sample tests](#one--and-two-sample-tests)
- [Confidence intervals](#confidence-intervals)
- [Power and sample size](#power-and-sample-size)
- [Regression](#regression)
- [ANOVA](#anova)
- [Correlation](#correlation)
- [Numerical analysis](#numerical-analysis)
- [Special functions](#special-functions)

### Distributions

#### Normal distribution

```javascript
var v = new Vector([0, 1, 2, 3])
var d = new Normal(0, 1).dens(v)
console.log(JSON.stringify(d, null, 4))
```

```javascript
{
    "elements": [
        0.3989422804014327,
        0.24197072451914337,
        0.05399096651318806,
        0.0044318484119380075
    ]
}
```

```javascript
var z = new Normal(0, 1).inverse(0.975)
console.log(z)
```

```javascript
1.959963986120195
```

#### T distribution

```javascript
var v = new Vector([-5, -4, -3])
var d = new T(100).distr(v)
console.log(JSON.stringify(d, null, 4))
```

```javascript
{
    "elements": [
        0.0000012250869359284488,
        0.00006076182218810418,
        0.001703957671686302
    ]
}
```

#### Kolmogorov distribution

```javascript
var k = new Kolmogorov()
console.log(k.distr(1))
console.log(k.inverse(0.45586))
```

```javascript
0.7300003283226454
0.800001482013613
```

#### Shapiro-Wilk test

```javascript
var v = new Vector([1, 2, 3, 4, 20])
console.log(JSON.stringify(Normality.shapiroWilk(v), null, 4))
```

```javascript
{
    "w": 0.6875792251194642,
    "p": 0.007068598509119006
}
```

#### Empirical distribution function

```javascript
var v = new Vector([-15.4, -8.8, 8.2, 3.4, -7.1, 4.5, -12.7, 5.2, -10.6, -11.2])
console.log(v.ecdf(-20))
console.log(v.ecdf(-2))
console.log(v.ecdf(8.2))
```

```
0
0.6
1
```

### One- and two-sample tests

#### Two-sample Student's T-test

```javascript
var first = new Vector([
  26, 21, 22, 26, 19, 22, 26, 25, 24, 21, 23, 23, 18, 29, 22,
])
var second = new Vector([
  18, 23, 21, 20, 20, 29, 20, 16, 20, 26, 21, 25, 17, 18, 19,
])
var t = StudentT.test(first, second)
console.log(JSON.stringify(t, null, 4))
```

```javascript
{
    "se": 1.1861636172906869,
    "t": 1.910922433992667,
    "df": 28,
    "p": 0.06630238610019434
}
```

#### Two-sample Kolmogorov-Smirnov test

```javascript
var x = new Vector([7.6, 8.4, 8.6, 8.7, 9.3, 9.9, 10.1, 10.6, 11.2])
var y = new Vector([
  5.2, 5.7, 5.9, 6.5, 6.8, 8.2, 9.1, 9.8, 10.8, 11.3, 11.5, 12.3, 12.5, 13.4,
  14.6,
])

console.log(JSON.stringify(new Nonparametric.kolmogorovSmirnov(x, y), null, 4))
```

```javascript
{
    "d": 0.4,
    "ks": 0.9486832980505139,
    "p": 0.3291047890978148
}
```

### Confidence intervals

```javascript
var v = new Vector([
  44617, 7066, 17594, 2726, 1178, 18898, 5033, 37151, 4514, 4000,
])
console.log(Confidence.normal(v, 0.95))
```

```javascript
;[3299.8678459441107, 25255.53215405589]
```

```javascript
var v = new Vector([
  44617, 7066, 17594, 2726, 1178, 18898, 5033, 37151, 4514, 4000,
])
console.log(Confidence.normalUpper(v, 0.95))
```

```javascript
23173.45950875796
```

### Power and sample size

```javascript
console.log(Power.sampleSize(0.05, 0.8, 0.72, 0.15))
```

```javascript
361.67637834828054
```

### Regression

#### Simple linear regression

```javascript
var y = new Vector([2000, 2001, 2002, 2003, 2004])
var r = new Vector([9.34, 8.5, 7.62, 6.93, 6.6])
var lm = Regression.linear(y, r)
console.log(JSON.stringify(lm, null, 4))
```

```javascript
{
    "n": 5,
    "slope": -0.7050000000000001,
    "intercept": 1419.208,
    "rse": 0.2005243127403941,
    "slope_se": 0.06341135544995657,
    "slope_t": -11.117882514849835,
    "slope_p": 0.00155918701775426,
    "intercept_se": 126.94956528481282,
    "intercept_t": 11.17930570944446,
    "intercept_p": 0.0015341064002789562,
    "rs": 0.9763046860267774
}
```

### ANOVA

#### One-way ANOVA

```javascript
var folate = new Vector([
  243, 251, 275, 291, 347, 354, 380, 392, 206, 210, 226, 249, 255, 273, 285,
  295, 309, 241, 258, 270, 293, 328,
])
var ventilation = new Factor([
  'N2O+O2,24h',
  'N2O+O2,24h',
  'N2O+O2,24h',
  'N2O+O2,24h',
  'N2O+O2,24h',
  'N2O+O2,24h',
  'N2O+O2,24h',
  'N2O+O2,24h',
  'N2O+O2,op',
  'N2O+O2,op',
  'N2O+O2,op',
  'N2O+O2,op',
  'N2O+O2,op',
  'N2O+O2,op',
  'N2O+O2,op',
  'N2O+O2,op',
  'N2O+O2,op',
  'O2,24h',
  'O2,24h',
  'O2,24h',
  'O2,24h',
  'O2,24h',
])
console.log(JSON.stringify(Anova.oneway(ventilation, folate), null, 4))
```

```javascript
{
    "tdf": 2,
    "tss": 15515.766414141408,
    "tms": 7757.883207070704,
    "edf": 19,
    "ess": 39716.09722222222,
    "ems": 2090.3209064327484,
    "f": 3.7113359882669754,
    "p": 0.04358933495917705
}
```

### Correlation

```javascript
var g = new Vector([
  8.3, 8.6, 8.8, 10.5, 10.7, 10.8, 11.0, 11.0, 11.1, 11.2, 11.3, 11.4, 11.4,
  11.7, 12.0, 12.9, 12.9, 13.3, 13.7, 13.8, 14.0, 14.2, 14.5, 16.0, 16.3, 17.3,
  17.5, 17.9, 18.0, 18.0, 20.6,
])
var h = new Vector([
  70, 65, 63, 72, 81, 83, 66, 75, 80, 75, 79, 76, 76, 69, 75, 74, 85, 86, 71,
  64, 78, 80, 74, 72, 77, 81, 82, 80, 80, 80, 87,
])
console.log(JSON.stringify(Correlation.pearson(g, h), null, 4))
```

```javascript
{
    "r": 0.5192800719499371,
    "t": 3.27216859079223,
    "df": 29,
    "p": 0.002757814793822755
}
```

### Numerical analysis

#### Adaptive Simpson

```javascript
var area = Numeric.adaptiveSimpson(
  function (x) {
    return Math.pow(x, x)
  },
  0,
  1,
  0.000000000001,
  20,
)
console.log(area)
```

```javascript
0.7834305107121379
```

#### Root finding (secant method)

```javascript
console.log(Numeric.secant(Math.sin, 3, 4))
```

```javascript
3.1415926535897647
```

#### Root finding (bisection method)

```javascript
console.log(Numeric.bisection(Math.sin, 3, 4))
```

```javascript
3.1415926539339125
```

### Special functions

#### Beta function

```javascript
console.log(Misc.beta(2, 2))
console.log(Misc.ibeta(0.2, 2, 2))
console.log(Misc.rbeta(0.2, 2, 2))
```

```javascript
0.16666666666666655
0.017333333333333333
0.10400000000000006
```

#### Gamma function

```javascript
console.log(Misc.gamma(0.5))
```

```javascript
1.7724538509055159
```

#### Error function

```javascript
console.log(Misc.erf(1))
```

```javascript
0.842700793
```