lognormális

The log-normal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. In simpler terms, if a random variable X follows a log-normal distribution, then its natural logarithm, ln(X), follows a normal distribution. This means that X can only take positive values.

The probability density function (PDF) of a log-normal distribution is given by a formula involving the mean and standard deviation of the underlying normal distribution. This distribution is characterized by its skewness, meaning it is not symmetric like the normal distribution. It has a long tail towards higher values.

The log-normal distribution arises naturally in many fields where quantities are formed by the product of many independent positive random variables. Examples include the distribution of income, the size of particles in a dust cloud, and the prices of financial assets. It is also used to model phenomena where growth rates are multiplicative rather than additive. Due to its positive-valued nature and right-skewed shape, it is a useful alternative to the normal distribution when dealing with such data.