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Miha Kralj
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lib/numerics/lognormdist/Lognormdist.md
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| **PineScript** | [lognormdist.pine](lognormdist.pine) |
- The Log-Normal Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the log-normal distribution, pro...
- Parameterized by `mu` (default 0.0), `sigma` (default 1.0), `period` (default 14).
- Output range: Varies (see docs).
- Requires `period` bars of warmup before first valid output (IsHot = true).
- **Trading note:** Log-normal distribution; models multiplicative processes like returns. Foundation of Black-Scholes.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
The Log-Normal Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the log-normal distribution, producing an output in $[0, 1]$. A random variable $X$ is log-normally distributed when $\ln(X)$ follows a normal distribution. This makes the log-normal CDF natural for financial data, where multiplicative returns (log-returns) are approximately normally distributed. The indicator min-max normalizes the source to $(0, 1]$, takes the natural logarithm, standardizes by parameters $\mu$ and $\sigma$, then evaluates the standard normal CDF. The result emphasizes values near the bottom of the recent range (where the logarithm diverges) and compresses values near the top.
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- Aitchison, J. & Brown, J.A.C. "The Lognormal Distribution." Cambridge University Press, 1957.
- Black, F. & Scholes, M. "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, 1973.
- Abramowitz, M. & Stegun, I. "Handbook of Mathematical Functions." NBS Applied Mathematics Series 55, 1964. Formula 7.1.26.
- Limpert, E., Stahel, W. & Abbt, M. "Log-normal Distributions across the Sciences: Keys and Clues." BioScience, 2001.
- Limpert, E., Stahel, W. & Abbt, M. "Log-normal Distributions across the Sciences: Keys and Clues." BioScience, 2001.