LOGNORMAL DISTRIBUTION Meaning and
Definition
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A lognormal distribution refers to a probability distribution in which the logarithm of a random variable follows a normal distribution. This type of distribution is commonly used in finance, economics, and various fields of science to model variables that are inherently positive and skewed to the right, such as stock prices, income, or population sizes.
In more detail, the lognormal distribution is characterized by two parameters: the location parameter μ and the shape parameter σ. The location parameter represents the mean of the logarithm of the random variable, while the shape parameter represents its standard deviation. The actual values of the random variable are obtained by exponentiating the corresponding values of the normal distribution.
The lognormal distribution exhibits several important properties. First, it has a strictly positive range, as the logarithm of any value less than or equal to zero is undefined. Second, it is asymmetrical and positively skewed, meaning that it has a longer right tail. Finally, it is unbounded, meaning there is no upper limit to the values it can take.
The lognormal distribution finds extensive applications in risk modeling, option pricing, and modeling of asset returns, among others. It is used to capture the behavior of variables that grow multiplicatively over time, where relative changes in value are more important than absolute ones.
Common Misspellings for LOGNORMAL DISTRIBUTION
- kognormal distribution
- pognormal distribution
- oognormal distribution
- lignormal distribution
- lkgnormal distribution
- llgnormal distribution
- lpgnormal distribution
- l0gnormal distribution
- l9gnormal distribution
- lofnormal distribution
- lovnormal distribution
- lobnormal distribution
- lohnormal distribution
- loynormal distribution
- lotnormal distribution
- logbormal distribution
- logmormal distribution
- logjormal distribution
- loghormal distribution
- lognirmal distribution
Etymology of LOGNORMAL DISTRIBUTION
The term "lognormal distribution" originates from the combination of two words: "logarithm" and "normal distribution".
1. Logarithm: The word "logarithm" comes from the Greek words "logos", meaning "ratio" or "proportion", and "arithmos", meaning "number". It refers to a mathematical function representing the exponent or power to which a fixed number (base) must be raised to obtain a given number. The logarithm of a number expresses the exponent to which the base must be raised.
2. Normal distribution: The term "normal distribution" or "Gaussian distribution" comes from the concept of a "normal curve", which was first introduced by Carl Friedrich Gauss, a German mathematician, in the early 19th century. The normal distribution is a continuous probability distribution that is symmetric around the mean, with most values clustered around the mean and few extreme values.
