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

Abstract

Generation algorithms of record times and values obtained from sequences of independent and non-identically distributed random variables which distribution functions are defined on a common support are proposed in the present paper. Known algorithms of generation of record times and values are given in introduction for the case when the initial random variables are independent and identically distributed. The brief review of scientific literature associated with this topic is also given in Introduction. It is also pointed out there that all efficient algorithms of record generation are based on the Markov property of records. In Section 2 the distribution functions of record times and values are derived for the case when the initial random variables are independent and non-identically distributed. The corresponding record generation algorithms are for the first time proposed. These algorithms are based on the derived distributions and the Markov property of records that also holds in the case when the initial observations are independent but non-identically distributed. In the end of this work in Section 3 the proposed algorithms are tested by simulation experiments. In these experiments the records are generated for the case when the initial random variables have the Gumbel distribution functions​

Keywords:

records, Gumbel distribution function, inverse-transform method, rejection method, generation algorithms, elapsed time​​