lognormální

Lognormální is a term used in statistics and probability theory to describe a probability distribution of a random variable whose logarithm is normally distributed. This distribution is often used to model phenomena where the variable can take only positive values and the logarithm of the variable is symmetrically distributed around its mean.

The lognormal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ) of the underlying normal distribution. The probability density function (PDF) of a lognormal distribution is given by:

f(x; μ, σ) = (1 / (x * σ * √(2π))) * exp(-(ln(x) - μ)^2 / (2σ^2))

for x > 0.

One of the key properties of the lognormal distribution is that it is right-skewed, meaning that the tail on the right side of the distribution is longer than the left side. This makes it suitable for modeling variables that are bounded below by zero and have a skewed distribution, such as income, asset prices, and lifetimes.

The lognormal distribution is also used in various fields, including finance, biology, and engineering, to model and analyze data that exhibit this type of behavior. It is important to note that the lognormal distribution is not the same as the normal distribution, even though the logarithm of a lognormally distributed variable is normally distributed. The two distributions have different shapes and properties.