Simulation of records obtained from sequences of independent and non-identically distributed variables

Abstract

In the present paper, we provide the density-mass functions of record times and values obtained from samples of independent and non-identically distributed random variables. By making use of these density-mass functions, we then present a record generation algorithm for the non-identical case. This algorithm was first proposed in the paper of S. A. Petukhov and A. V. Stepanov (2023) Generation of records obtained from sequences of independent and non-identically distributed random variables. Vestnik St. Petersburg University, Mathematics 56 (4):540–8 in a more complicated form. The algorithm applies the Markovian property of records, which is known in the case when the initial observations are independent and identically distributed and which extends to the non-identical case. Later in the paper, we test the proposed algorithm by conducting simulation experiments with exponential and normal variables.