LOGNORMAL Meaning and
Definition
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The term "lognormal" refers to a statistical distribution that is derived from the logarithm of a random variable. In essence, it describes a probability distribution where the logarithm of the variable follows a normal distribution. The lognormal distribution is often used to model naturally occurring phenomena that cannot take negative values, such as prices, incomes, or stock returns.
In a lognormal distribution, the values of the variable are positively skewed, meaning they have a longer tail on the right side of the distribution. The shape of the distribution is influenced by two parameters: the mean and standard deviation of the logarithm of the variable. The mean affects the location of the peak of the distribution, while the standard deviation governs the spread or dispersion of the values.
One of the key properties of a lognormal distribution is that it guarantees only positive values for the variable being modeled. This is because the logarithm of any positive value is always a real number. Consequently, the lognormal distribution is often used in finance and economics to analyze variables that are strictly positive, such as stock prices, asset returns, or the growth rates of economic variables.
By employing the lognormal distribution, researchers and practitioners can make reliable predictions and estimates when dealing with variables constrained to positive values, which would be inappropriate to model using symmetric normal distributions.
Etymology of LOGNORMAL
The term "lognormal" is derived from two words: "logarithm" and "normal".
The word "logarithm" refers to a mathematical function that gives the exponent to which a base must be raised to obtain a certain number. It is often abbreviated as "log" and is used to convert exponential relationships into linear ones.
The word "normal" in statistics refers to the normal distribution, also known as the Gaussian distribution or the bell curve. This distribution is commonly used to model many natural phenomena as it follows a specific shape and has certain statistical properties.
When combined, "logarithm" and "normal" give rise to the term "lognormal", which is used to describe a probability distribution of a random variable whose logarithm follows a normal distribution. In simpler terms, if the natural logarithm of a variable is normally distributed, then the variable itself is said to have a lognormal distribution.
