LognormalVerteilungen

LogNormalverteilungen (also known as Lognormal distributions) are a type of probability distribution used to model phenomena that exhibit extreme values. They are a continuous probability distribution of a random variable whose logarithm is normally distributed. The LogNormal distribution is a convenient way to model data that is skewed to the right, such as income, wealth, and stock prices.

In a LogNormal distribution, the variable of interest (usually denoted as X) is transformed into a new variable Y, which is the natural logarithm of X. If Y is a normally distributed variable, then its probability distribution is called the normal distribution. This means that knowing the probability distribution of Y (the logarithm of X), one can infer the probability distribution of X (the original variable).

The LogNormal distribution has a few key properties. Firstly, it has a skewed shape, with a longer tail on the right side. This makes it suitable for modeling phenomena where extreme values are more likely. Secondly, the distribution is characterized by two parameters: the shape parameter (σ^2) and the scale parameter (μ). The shape parameter determines the spread of the distribution, while the scale parameter determines its position.

LogNormal distributions have applications in various fields, including finance (to model stock prices and returns), economics (to model income and wealth), and engineering (to model failure times of complex systems). The distribution is widely used in data analysis and machine learning to model and predict phenomena with extreme values.