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.
오픈 소스 스크립트
진정한 트레이딩뷰 정신에 따라 이 스크립트 작성자는 트레이더가 기능을 검토하고 검증할 수 있도록 오픈소스로 공개했습니다. 작성자에게 찬사를 보냅니다! 무료로 사용할 수 있지만 코드를 다시 게시할 경우 하우스 룰이 적용된다는 점을 기억하세요.
Premium Indicator: patreon.com/c/NEUROPULSE_TRADE
Discord: discord.gg/NZuBAnR3
Discord: discord.gg/NZuBAnR3
면책사항
이 정보와 게시물은 TradingView에서 제공하거나 보증하는 금융, 투자, 거래 또는 기타 유형의 조언이나 권고 사항을 의미하거나 구성하지 않습니다. 자세한 내용은 이용 약관을 참고하세요.
오픈 소스 스크립트
진정한 트레이딩뷰 정신에 따라 이 스크립트 작성자는 트레이더가 기능을 검토하고 검증할 수 있도록 오픈소스로 공개했습니다. 작성자에게 찬사를 보냅니다! 무료로 사용할 수 있지만 코드를 다시 게시할 경우 하우스 룰이 적용된다는 점을 기억하세요.
Premium Indicator: patreon.com/c/NEUROPULSE_TRADE
Discord: discord.gg/NZuBAnR3
Discord: discord.gg/NZuBAnR3
면책사항
이 정보와 게시물은 TradingView에서 제공하거나 보증하는 금융, 투자, 거래 또는 기타 유형의 조언이나 권고 사항을 의미하거나 구성하지 않습니다. 자세한 내용은 이용 약관을 참고하세요.