Log-Normal Distribution


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.

BREAKING DOWN '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.

  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. Probability Distribution

    A statistical function that describes all the possible values ...
  4. Normal Distribution

    A probability distribution that plots all of its values in a ...
  5. Kurtosis

    A statistical measure used to describe the distribution of observed ...
  6. Random Walk Theory

    The theory that stock price changes have the same distribution ...
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. Investing

    What a Family Tradition Taught Me About Investing

    We share some lessons from friends and family on saving money and planning for retirement.
  9. Investing

    Where the Price is Right for Dividends

    There are two broad schools of thought for equity income investing: The first pays the highest dividend yields and the second focuses on healthy yields.
  10. Personal Finance

    How Tech Can Help with 3 Behavioral Finance Biases

    Even if you’re a finance or statistics expert, you’re not immune to common decision-making mistakes that can negatively impact your finances.
  1. Is Colombia an emerging market economy?

    Colombia meets the criteria of an emerging market economy. The South American country has a much lower gross domestic product, ... Read Full Answer >>
  2. What assumptions are made when conducting a t-test?

    The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality ... Read Full Answer >>
  3. What is the utility function and how is it calculated?

    In economics, utility function is an important concept that measures preferences over a set of goods and services. Utility ... Read Full Answer >>
  4. What are some of the more common types of regressions investors can use?

    The most common types of regression an investor can use are linear regressions and multiple linear regressions. Regressions ... Read Full Answer >>
  5. What types of assets lower portfolio variance?

    Assets that have a negative correlation with each other reduce portfolio variance. Variance is one measure of the volatility ... Read Full Answer >>
  6. When is it better to use systematic over simple random sampling?

    Under simple random sampling, a sample of items is chosen randomly from a population, and each item has an equal probability ... Read Full Answer >>

You May Also Like

Hot Definitions
  1. Take A Bath

    A slang term referring to the situation of an investor who has experienced a large loss from an investment or speculative ...
  2. Black Friday

    1. A day of stock market catastrophe. Originally, September 24, 1869, was deemed Black Friday. The crash was sparked by gold ...
  3. Turkey

    Slang for an investment that yields disappointing results or turns out worse than expected. Failed business deals, securities ...
  4. Barefoot Pilgrim

    A slang term for an unsophisticated investor who loses all of his or her wealth by trading equities in the stock market. ...
  5. Quick Ratio

    The quick ratio is an indicator of a company’s short-term liquidity. The quick ratio measures a company’s ability to meet ...
  6. Black Tuesday

    October 29, 1929, when the DJIA fell 12% - one of the largest one-day drops in stock market history. More than 16 million ...
Trading Center