The advances in science and technology have led to vast amounts of complex and heterogeneous data from multiple sources of random sample length. This paper aims to investigate the extreme behavior of competing risks with random sample sizes. Two accelerated mixed types of stable distributions are obtained as the extreme limit laws of random sampling competing risks under linear and power normalizations, respectively. The theoretical findings are well illustrated by typical examples and numerical studies. The developed methodology and models provide new insights into modeling complex data across numerous fields.
