mirror of
https://github.com/metabarcoding/obitools4.git
synced 2026-04-30 12:00:39 +00:00
31 lines
1.6 KiB
Markdown
31 lines
1.6 KiB
Markdown
|
# `obistats` Package: Normal Distribution Utilities
|
|||
|
|
|
|||
|
|
The `obistats` package provides a lightweight, efficient implementation of the **normal (Gaussian) distribution**, including core statistical operations.
|
|||
|
|
|
|||
|
|
## Core Type
|
|||
|
|
- `NormalDist`: Represents a normal distribution with parameters:
|
|||
|
|
- `Mu` (mean)
|
|||
|
|
- `Sigma` (standard deviation)
|
|||
|
|
|
|||
|
|
## Predefined Constants
|
|||
|
|
- `StdNormal`: A standard normal distribution (`Mu = 0`, `Sigma = 1`).
|
|||
|
|
- `invSqrt2Pi`: Precomputed constant for performance optimization.
|
|||
|
|
|
|||
|
|
## Key Methods
|
|||
|
|
| Method | Description |
|
|||
|
|
|--------|-------------|
|
|||
|
|
| `PDF(x)` | Computes the **probability density function** at point `x`. |
|
|||
|
|
| `pdfEach(xs [])` | Vectorized PDF evaluation over a slice of values (optimized for standard normal). |
|
|||
|
|
| `CDF(x)` | Computes the **cumulative distribution function** at point `x` via error function (`erfc`). |
|
|||
|
|
| `cdfEach(xs [])` | Vectorized CDF evaluation over a slice. |
|
|||
|
|
| `InvCDF(p)` | Computes the **inverse CDF (quantile function)** using Acklam’s algorithm with refinement. Handles edge cases (`p = 0`, `1`) and numerical stability. |
|
|||
|
|
| `Rand(r *rand.Rand)` | Generates a random sample from the distribution (uses Go’s built-in `NormFloat64`). |
|
|||
|
|
| `Bounds()` | Returns a practical support interval: `[Mu − 3·Sigma, Mu + 3·Sigma]` (≈99.7% coverage). |
|
|||
|
|
|
|||
|
|
## Implementation Notes
|
|||
|
|
- Optimized paths for standard normal (`Mu = 0`, `Sigma = 1`) reduce computation cost.
|
|||
|
|
- Uses Go’s standard math library (`math.Erfc`, `math.Log`, etc.).
|
|||
|
|
- Designed for performance and numerical accuracy in statistical applications.
|
|||
|
|
|
|||
|
|
> *Note: Duplicates functionality from an internal module (`bench`), likely for reuse in public packages.*
|