OPEN-SOURCE SCRIPT
Logit Transform -EasyNeuro-

Logit Transform
This script implements a novel indicator inspired by the Fisher Transform, replacing its core arctanh-based mapping with the logit transform. It is designed to highlight extreme values in bounded inputs from a probabilistic and statistical perspective.
Background: Fisher Transform
The Fisher Transform, introduced by John Ehlers, is a statistical technique that maps a bounded variable x (between a and b) to a variable approximately following a Gaussian distribution. The standard form for a normalized input y (between -1 and 1) is F(y) = 0.5 * ln((1 + y)/(1 - y)) = arctanh(y).
This transformation has the following properties:
Linearization of extremes:
Small deviations around the mean are smooth, while movements near the boundaries are sharply amplified.
Gaussian approximation:
After transformation, the variable approximates a normal distribution, enabling analytical techniques that assume normality.
Probabilistic interpretation:
The Fisher Transform can be linked to likelihood ratio tests, where the transform emphasizes deviations from median or expected values in a statistically meaningful way.
In technical analysis, this allows traders to detect turning points or extreme market conditions more clearly than raw oscillators alone.
Logit Transform as a Generalization
The logit function is defined for p between 0 and 1 as logit(p) = ln(p / (1 - p)).
Key properties of the logit transform:
From a statistical viewpoint, the logit transform corresponds to the canonical link function in binomial generalized linear models (GLMs). This provides a natural interpretation of the transformed variable as the logarithm of the likelihood ratio between success and failure states, giving a rigorous probabilistic framework for extreme value detection.
Theoretical Advantages
Distributional linearization:
For inputs that can be interpreted as probabilities, the logit transform creates a variable approximately linear in log-odds, similar to Fisher’s goal of Gaussianization but with a probabilistic foundation.
Extreme sensitivity:
By amplifying small differences near 0 or 1, it allows for sharper detection of market extremes or overbought/oversold conditions.
Statistical interpretability:
Provides a link to statistical hypothesis testing via likelihood ratios, enabling integration with probabilistic models or risk metrics.
Applications in Technical Analysis
Oscillator enhancement:
Apply to RSI, Stochastic Oscillators, or other bounded indicators to accentuate extreme values with a well-defined probabilistic interpretation.
Comparative study:
Use alongside the Fisher Transform to analyze the effect of different nonlinear mappings on market signals, helping to uncover subtle nonlinearity in price behavior.
Probabilistic risk assessment:
Transforming input series into log-odds allows incorporation into statistical risk models or volatility estimation frameworks.
Practical Considerations
The logit diverges near 0 and 1, requiring careful scaling or smoothing to avoid numerical instability. As with the Fisher Transform, this indicator is not a standalone trading signal and should be combined with complementary technical or statistical indicators.
In summary, the Logit Transform builds upon the Fisher Transform’s theoretical foundation while introducing a probabilistically rigorous mapping. By connecting extreme-value detection to odds ratios and likelihood principles, it provides traders and analysts with a mathematically grounded tool for examining market dynamics.
This script implements a novel indicator inspired by the Fisher Transform, replacing its core arctanh-based mapping with the logit transform. It is designed to highlight extreme values in bounded inputs from a probabilistic and statistical perspective.
Background: Fisher Transform
The Fisher Transform, introduced by John Ehlers, is a statistical technique that maps a bounded variable x (between a and b) to a variable approximately following a Gaussian distribution. The standard form for a normalized input y (between -1 and 1) is F(y) = 0.5 * ln((1 + y)/(1 - y)) = arctanh(y).
This transformation has the following properties:
Linearization of extremes:
Small deviations around the mean are smooth, while movements near the boundaries are sharply amplified.
Gaussian approximation:
After transformation, the variable approximates a normal distribution, enabling analytical techniques that assume normality.
Probabilistic interpretation:
The Fisher Transform can be linked to likelihood ratio tests, where the transform emphasizes deviations from median or expected values in a statistically meaningful way.
In technical analysis, this allows traders to detect turning points or extreme market conditions more clearly than raw oscillators alone.
Logit Transform as a Generalization
The logit function is defined for p between 0 and 1 as logit(p) = ln(p / (1 - p)).
Key properties of the logit transform:
- Maps probabilities in (0, 1) to the entire real line, similar to the Fisher Transform.
- Emphasizes values near 0 and 1, providing sharp differentiation of extreme states.
- Directly interpretable in terms of odds and likelihood ratios: logit(p) = ln(odds).
From a statistical viewpoint, the logit transform corresponds to the canonical link function in binomial generalized linear models (GLMs). This provides a natural interpretation of the transformed variable as the logarithm of the likelihood ratio between success and failure states, giving a rigorous probabilistic framework for extreme value detection.
Theoretical Advantages
Distributional linearization:
For inputs that can be interpreted as probabilities, the logit transform creates a variable approximately linear in log-odds, similar to Fisher’s goal of Gaussianization but with a probabilistic foundation.
Extreme sensitivity:
By amplifying small differences near 0 or 1, it allows for sharper detection of market extremes or overbought/oversold conditions.
Statistical interpretability:
Provides a link to statistical hypothesis testing via likelihood ratios, enabling integration with probabilistic models or risk metrics.
Applications in Technical Analysis
Oscillator enhancement:
Apply to RSI, Stochastic Oscillators, or other bounded indicators to accentuate extreme values with a well-defined probabilistic interpretation.
Comparative study:
Use alongside the Fisher Transform to analyze the effect of different nonlinear mappings on market signals, helping to uncover subtle nonlinearity in price behavior.
Probabilistic risk assessment:
Transforming input series into log-odds allows incorporation into statistical risk models or volatility estimation frameworks.
Practical Considerations
The logit diverges near 0 and 1, requiring careful scaling or smoothing to avoid numerical instability. As with the Fisher Transform, this indicator is not a standalone trading signal and should be combined with complementary technical or statistical indicators.
In summary, the Logit Transform builds upon the Fisher Transform’s theoretical foundation while introducing a probabilistically rigorous mapping. By connecting extreme-value detection to odds ratios and likelihood principles, it provides traders and analysts with a mathematically grounded tool for examining market dynamics.
Script de código abierto
Siguiendo fielmente el espíritu de TradingView, el creador de este script lo ha publicado en código abierto, permitiendo que otros traders puedan revisar y verificar su funcionalidad. ¡Enhorabuena al autor! Puede utilizarlo de forma gratuita, pero tenga en cuenta que la publicación de este código está sujeta a nuestras Normas internas.
Premium Indicator: patreon.com/c/NEUROPULSE_TRADE
Discord: discord.gg/NZuBAnR3
Discord: discord.gg/NZuBAnR3
Exención de responsabilidad
La información y las publicaciones que ofrecemos, no implican ni constituyen un asesoramiento financiero, ni de inversión, trading o cualquier otro tipo de consejo o recomendación emitida o respaldada por TradingView. Puede obtener información adicional en las Condiciones de uso.
Script de código abierto
Siguiendo fielmente el espíritu de TradingView, el creador de este script lo ha publicado en código abierto, permitiendo que otros traders puedan revisar y verificar su funcionalidad. ¡Enhorabuena al autor! Puede utilizarlo de forma gratuita, pero tenga en cuenta que la publicación de este código está sujeta a nuestras Normas internas.
Premium Indicator: patreon.com/c/NEUROPULSE_TRADE
Discord: discord.gg/NZuBAnR3
Discord: discord.gg/NZuBAnR3
Exención de responsabilidad
La información y las publicaciones que ofrecemos, no implican ni constituyen un asesoramiento financiero, ni de inversión, trading o cualquier otro tipo de consejo o recomendación emitida o respaldada por TradingView. Puede obtener información adicional en las Condiciones de uso.