lognormalny

The term "lognormalny" translates from Polish to English as "lognormal". It refers to a probability distribution of a random variable whose logarithm is normally distributed. In simpler terms, if a variable X follows a lognormal distribution, then the natural logarithm of X, denoted as ln(X), follows a normal distribution.

The lognormal distribution is characterized by two parameters, often denoted as mu (μ) and sigma (σ). Mu represents the mean of the logarithm of the variable, and sigma represents the standard deviation of the logarithm. The shape of the lognormal distribution is typically skewed to the right, meaning it has a long tail on the right side.

This distribution is commonly encountered in fields where variables are multiplicative in nature or are the result of many small, independent multiplicative effects. Examples include the distribution of income, the size of particles in a material, the duration of certain biological processes, and the prices of financial assets.

Unlike the normal distribution, the mean, median, and mode of a lognormal distribution are generally not the same. The median is equal to the exponential of the mean of the logarithm (e^μ), while the mean is e^(μ + σ²/2). The variance is also dependent on these parameters.

The lognormal distribution is a continuous probability distribution and is always positive, meaning the random variable can only take on positive values. This property makes it suitable for modeling quantities that cannot be negative, such as measurements of size, concentration, or time.