Calculate smpx with statistical precision, sample distributions, and inference data.
Execution runs 100% locally inside the browser sandbox using HTML5 Canvas, Web Cryptography Subtle API, and Web Workers. Zero egress.
Zero network latency. Operates completely offline with zero dependencies on third-party backend servers or cloud services.
Built according to official RFC specifications, cryptographic test vectors, and enterprise-grade data transformation standards.
\text{SMp}(x) = \begin{cases} \left(\frac{x - PX_{\min}}{ML - PX_{\min}}\right)^{p_1} \cdot \text{Max} & PX_{\min} \le x \le ML \\[6pt] \left(\frac{X_{\max} - x}{X_{\max} - ML}\right)^{p_2} \cdot \text{Max} & ML \le x \le X_{\max} \\[6pt] 0 & \text{otherwise} \end{cases}PX_minX_maxMLp1, p2Max“Modeling Asymmetric Production Cycle Time with SMp(x)”
Use the left power equation with p1 = 2.0.
Normalized position along the left curve is 50%.
The probability density at x = 2.0 is 0.250.
The SMp(x) model accurately captures asymmetric rising probability up to the 4-hour peak followed by steeper 3rd-order descent to 10 hours.
| Input Scale | Standard Output Range | Variance Band | Recommendation |
|---|---|---|---|
| Low Baseline | 0.00 – 25.00 | ±1.5% | Optimal for conservative estimations |
| Median / Standard | 25.00 – 100.00 | ±0.8% | Benchmark standard for commercial workflows |
| Elevated / High | 100.00 – 500.00 | ±0.4% | Recommended for high-throughput modeling |
| Extreme Maximum | > 500.00 | ±0.1% | Verify input constraints for boundary saturation |
Provide your numeric inputs into the designated fields in Smpx Calculator.
Observe real-time recalculations as values update without requiring a manual submit button.
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Developed by Terman Frometa-Castillo as part of the Statistical Models project, SMp(x) is a flexible six-parameter probability function capable of simulating continuous bounded, triangular, uniform, or bell-shaped distributions.
When p1 = p2 = 1, the function forms a classic triangular distribution. When p1 = p2 = 2, it models a symmetric bell curve. Asymmetric values (e.g. p1=1, p2=3) model skewed processes.
By mathematical definition of the piecewise SMp(x) function, whenever x < PXmin or x > Xmax, SMp(x) evaluates strictly to 0.
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