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40 lines
3.6 KiB
Markdown
40 lines
3.6 KiB
Markdown
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# Numerics
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> "Price is raw signal. Transform exposes hidden structure. Derivative reveals momentum. Normalization enables comparison. Mathematics is lens, not oracle."
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Basic mathematical transforms and utility functions for time series. These building blocks convert raw price data into forms suitable for analysis, comparison, and downstream indicator consumption.
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## Implementation Status
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| Indicator | Full Name | Status | Description |
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| :--- | :--- | :---: | :--- |
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| [ACCEL](accel/Accel.md) | Acceleration | ✓ | Momentum change; second derivative of price. |
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| BETADIST | Beta Distribution | ≡ | Continuous probability distribution defined on interval [0, 1] |
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| BINOMDIST | Binomial Distribution | ≡ | Discrete probability distribution of successes in n independent trials |
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| [CHANGE](change/Change.md) | Percentage Change | ✓ | Relative price movement over lookback period. |
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| CWT | Continuous Wavelet Transform | ≡ | Analyzes time series data across different frequency scales continuously |
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| DIFF | Difference | ≡ | Calculates the simple difference between current and previous values |
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| DWT | Discrete Wavelet Transform | ≡ | Analyzes time series data across different frequency scales at discrete intervals |
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| EXPDIST | Exponential Distribution | ≡ | Continuous probability distribution describing time between events |
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| [EXPTRANS](exptrans/Exptrans.md) | Exponential Transform | ✓ | e^x transform for log-space conversion reversal. |
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| FDIST | F-Distribution | ≡ | Continuous probability distribution ratio of two chi-squared distributions |
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| FFT | Fast Fourier Transform | ≡ | Efficient algorithm for computing the discrete Fourier transform and its inverse |
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| GAMMADIST | Gamma Distribution | ≡ | Continuous probability distribution generalizing exponential and chi-squared |
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| [HIGHEST](highest/Highest.md) | Rolling Maximum | ✓ | Maximum value over lookback window. |
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| IFFT | Inverse Fast Fourier Transform | ≡ | Efficient algorithm for computing the inverse discrete Fourier transform |
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| [JERK](jerk/Jerk.md) | Jerk | ✓ | Rate of acceleration; third derivative of price. |
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| [LINEARTRANS](lineartrans/Lineartrans.md) | Linear Transform | ✓ | y = ax + b scaling transformation. |
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| LOGNORMDIST | Log-normal Distribution | ≡ | Continuous probability distribution of a variable whose log is normally distributed |
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| [LOGTRANS](logtrans/Logtrans.md) | Logarithmic Transform | ✓ | Natural log for percentage-based analysis. |
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| [LOWEST](lowest/Lowest.md) | Rolling Minimum | ✓ | Minimum value over lookback window. |
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| [MIDPOINT](midpoint/Midpoint.md) | Midrange | ✓ | (Highest + Lowest) / 2 over lookback window. |
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| [NORMALIZE](normalize/Normalize.md) | Min-Max Normalization | ✓ | Scale to [0,1] range using rolling min/max. |
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| NORMDIST | Normal Distribution | ≡ | Gaussian bell-shaped probability distribution |
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| POISSONDIST | Poisson Distribution | ≡ | Discrete probability distribution expressing events in fixed time interval |
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| [RELU](relu/Relu.md) | Rectified Linear Unit | ✓ | max(0, x); neural network activation function. |
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| [SIGMOID](sigmoid/Sigmoid.md) | Logistic Function | ✓ | 1/(1+e^-x); bounded [0,1] transform. |
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| [SLOPE](slope/Slope.md) | Rate of Change | ✓ | First derivative; velocity of price movement. |
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| [SQRTTRANS](sqrttrans/Sqrttrans.md) | Square Root Transform | ✓ | Variance-stabilizing transformation. |
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| TDIST | Student's t-Distribution | ≡ | Continuous probability distribution when estimating mean of normally distributed population |
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| WEIBULLDIST | Weibull Distribution | ≡ | Continuous probability distribution useful in reliability and survival analysis |
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