convergence of distributions

Convergence of distributions describes how a sequence of probability distributions becomes increasingly similar to a specific distribution as more data or samples are considered. Imagine observing a process over time; as you gather more results, the overall pattern or spread of outcomes stabilizes and approaches a fixed distribution. This concept helps statisticians understand the long-term behavior of random processes, ensuring that, with enough data, the observed distributions reliably approximate a particular theoretical model. In essence, it's about the gradual alignment of probability patterns as more information is accumulated.