Distributionsskript

Distributionsskript is a German term that typically refers to a set of lecture notes or a course script focusing on probability distributions. It is commonly used in university contexts and by students for self-study, and it often serves as a structured introduction to the topic within statistics or data science curricula.

A distributionsskript usually covers both discrete and continuous distributions, starting from fundamental concepts such as random variables, probability mass functions, probability density functions, and cumulative distribution functions. It then presents common distribution families (for example Bernoulli, Binomial, Geometric, Poisson for discrete cases; Uniform, Normal, Exponential, Gamma, Beta, Cauchy, Student’s t, Log-normal for continuous cases) and discusses their parameters, shapes, and typical applications. Topics such as moments (mean, variance, skewness, kurtosis), moment generating functions, and basic transformations are often included, along with multivariate distributions and copulas for dependence structures.

Beyond definitions, a distributionsskript usually describes methods for describing data with distributions, including parameter estimation (notably maximum likelihood and method of moments), hypothesis testing related to distributional assumptions, and goodness-of-fit tests. It may also introduce sampling techniques (inverse transform, acceptance–rejection) and provide examples using software such as R or Python to illustrate simulation and data analysis.

The format of a distributionsskript can vary, ranging from compact notes to comprehensive textbooks or slide decks, frequently accompanied by exercises and solutions. It serves as a practical reference for students, educators, and practitioners seeking a focused overview of probability distributions and their applications in statistics and data science.