# NormalFit

> Samples pouring into a histogram, then the normal curve that fits them. samples is a slice, and shown (a tracker) says how many of them are binned so…

Page: https://fframes-kit.pages.dev/docs/math/normal-fit/
Cargo feature: `math` (`fframes-kit = { version = "..", features = ["math"] }`)

Samples pouring into a histogram, then the normal curve that fits them. `samples` is a
slice, and `shown` (a tracker) says how many of them are binned so far: `bins` bars over
`range` as a density, no taller than the top of the y range. The curve has the mean and
standard deviation of the samples shown and draws with `curve_enter`. With `stats` it writes
`n = 1500   mean 0.03   sd 1.01` at `stats_at` (pixels). `normal_samples(seed, n, mean, sd)`
gives the same samples for the same seed (the random bits match on every machine, the
logarithm and cosine may differ in the last bit); `mean_sd` and `normal_pdf` are the
numbers behind the curve. Gallery scenes: `NormalFit`, `HistogramToNormal`.

Gallery clip of `NormalFit`: https://fframes-kit.pages.dev/media/scenes/NormalFit-076344e4.mp4

Gallery clip of `HistogramToNormal`: https://fframes-kit.pages.dev/media/scenes/HistogramToNormal-7d291752.mp4

```rust
use fframes::animation::KeyFramesAnimation;
use fframes_kit::prelude::*;
use fframes_kit::kits::math::{mean_sd, normal_samples};

fn figure<'a>(
    ui: &mut Ui<'a, '_, '_>,
    samples: &'a [f64],
    shown: &'a KeyFramesAnimation<f32>,
) -> Svgr<'a> {
    let axes = Axes {
        x_range: Range::new(-3.0, 3.0, 1.0),
        y_range: Range::new(0.0, 0.5, 0.1),
        ..ui.defaults()
    };
    let map = axes.map(ui);
    let fit = ui.show(NormalFit {
        samples,
        shown: shown.into(),
        axes: map,
        range: (-3.0, 3.0),
        bins: 24,
        curve_enter: Some(Create { delay: 3.0, ..Default::default() }.into()),
        ..ui.defaults()
    });
    let axes = ui.show(axes);
    svgr!(<g>{axes}{fit}</g>)
}

let samples = normal_samples(7, 1500, 0.0, 1.0);
let (mean, sd) = mean_sd(&samples);
assert!(mean.abs() < 0.1 && (sd - 1.0).abs() < 0.1);
```

## API

Components are plain structs. Set the fields you need and fill the rest with `..ui.defaults()`: the defaults below come from the current theme (`theme.` values are fields of `Theme`).

### NormalFit

| Field | Type | Default | Description |
| --- | --- | --- | --- |
| `samples` | `&[f64]` | `&[]` | The sample values to bin; only the first `shown` of them count. |
| `shown` | `ValueTracker` | `0.0.into()` | How many of the samples are shown so far; a tracker, so they can pour in over time. |
| `axes` | `AxesMap` | `AxesMap::default()` | The axes (an `AxesMap`) the bars and the curve sit on; the bars are no taller than the top of its y range. |
| `range` | `(f64, f64)` | `(-3.0, 3.0)` | The values `(min, max)` the bars cover, in the axes' x units. |
| `bins` | `usize` | `24` | Number of bars the range is cut into; the bar heights are a density. |
| `fill` | `Color` | `theme.colors.accent` | Fill of the bars. |
| `curve_color` | `Color` | `theme.colors.highlight` | Colour of the fitted normal curve. |
| `curve_width` | `f32` | `theme.stroke.thick` | Width of the curve in pixels. |
| `curve_enter` | `Option<EnterAnim>` | `None` | How the curve appears; `None` shows it from the start. |
| `stats` | `bool` | `true` | Writes the mean and standard deviation of the samples shown at `stats_at` when `true`. |
| `stats_at` | `(f32, f32)` | `(1500.0, 300.0)` | Where the statistics are written, in pixels of the canvas. |
| `stats_enter` | `Option<FadeIn>` | `None` | Fade in of the statistics; `None` shows them from the start. |

Feature `math` · [Source](https://github.com/khanhthanhdev/fframes-kit/blob/main/fframes-kit/src/kits/math/normal.rs#L65)