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lib/numerics/sigmoid/Sigmoid.md
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# SIGMOID: Logistic Function
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Numeric |
| **Inputs** | Source (close) |
| **Parameters** | `k` (default 1.0), `x0` (default 0.0) |
| **Outputs** | Single series (Sigmoid) |
| **Output range** | Varies (see docs) |
| **Warmup** | `0` bars |
### TL;DR
- The Sigmoid (Logistic) transformer maps any real-valued input to the bounded range (0, 1) using the standard logistic function.
- Parameterized by `k` (default 1.0), `x0` (default 0.0).
- Output range: Varies (see docs).
- Requires `0` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The sigmoid function is the S-curve that turns messy reality into neat probabilities—a mathematical diplomat that insists every answer must be between 0 and 1."
The Sigmoid (Logistic) transformer maps any real-valued input to the bounded range (0, 1) using the standard logistic function. Its characteristic S-shaped curve makes it indispensable for probability estimation, neural network activations, and any scenario requiring bounded outputs from unbounded inputs.