Log-Normal Distribution

AAA

DEFINITION of 'Log-Normal Distribution'

A statistical distribution of random variables which have a normally distributed logarithm. Log-normal distributions can model a random variable X where log(X) is normally distributed.

These distributions, under multiplication and division, are self-replicating. That is to say, multiplying or dividing log-normal random variables will result in log-normal distributions.

INVESTOPEDIA EXPLAINS 'Log-Normal Distribution'

For example, log-normal distributions can model certain instances, such as the change in price distribution of a stock, or commodity positions. This is because the time series creates random variables. By taking the natural log of each of the random variables, the resulting set of numbers will be log-normally distributed. Other uses include survival rates of cancer patients or failure rates in product tests.

RELATED TERMS
  1. Euler's Constant

    The limit of the sum of 1 + 1/2 + 1/3 + 1/4 ... + 1/n, minus ...
  2. Poisson Distribution

    A statistical distribution showing the frequency probability ...
  3. Normal Distribution

    A probability distribution that plots all of its values in a ...
  4. Probability Distribution

    A statistical function that describes all the possible values ...
  5. Random Walk Theory

    The theory that stock price changes have the same distribution ...
  6. Kurtosis

    A statistical measure used to describe the distribution of observed ...
Related Articles
  1. Markets

    The Uses And Limits Of Volatility

    Check out how the assumptions of theoretical risk models compare to actual market performance.
  2. Active Trading

    What Is Market Efficiency?

    The efficient market hypothesis (EMH) suggests that stock prices fully reflect all available information in the market. Is this possible?
  3. Investing Basics

    Economic Indicators That Do-It-Yourself Investors Should Know

    Understanding these investing tools will put the market in your hands.
  4. Fundamental Analysis

    Find The Right Fit With Probability Distributions

    Discover a few of the most popular probability distributions and how to calculate them.
  5. Options & Futures

    Options Trading Volume And Open Interest

    Learn how these two statistics can give you an edge in trading options.
  6. Fundamental Analysis

    A Disaster-Protection Plan For Your Portfolio

    If you can't predict the future, you'll need to plan ahead to protect your assets from the impact of major world events.
  7. Active Trading

    Introduction To Stationary And Non-Stationary Processes

    What to know about stationary and non-stationary processes before you try to model or forecast.
  8. Fundamental Analysis

    What are the most common issues with Serial Correlation in stocks?

    Read about the concept of serial correlation in stock returns, and learn why market analysts are divided about the efficacy of trading based on stock patterns.
  9. Bonds & Fixed Income

    How do I calculate yield to maturity of a zero coupon bond?

    Find out how to calculate the yield to maturity for a zero coupon bond, and see why this calculation is more simple than a bond with a coupon.
  10. Trading Strategies

    How far back in a stock's history should you go when gauging its volatility?

    Discover why it can be difficult for investors to figure out how far back to go into a stock's history when gauging its volatility.

You May Also Like

Hot Definitions
  1. Weather Insurance

    A type of protection against a financial loss that may be incurred because of rain, snow, storms, wind, fog, undesirable ...
  2. Portfolio Turnover

    A measure of how frequently assets within a fund are bought and sold by the managers. Portfolio turnover is calculated by ...
  3. Commercial Paper

    An unsecured, short-term debt instrument issued by a corporation, typically for the financing of accounts receivable, inventories ...
  4. Federal Funds Rate

    The interest rate at which a depository institution lends funds maintained at the Federal Reserve to another depository institution ...
  5. Fixed Asset

    A long-term tangible piece of property that a firm owns and uses in the production of its income and is not expected to be ...
  6. Break-Even Analysis

    An analysis to determine the point at which revenue received equals the costs associated with receiving the revenue. Break-even ...
Trading Center