Varentropy of inactivity time of a random variable and its related applications

The information content of a random variable is of importance in the field of information theory. The mean and the variance of the information content of a random variable are called entropy and varentropy of this random variable, respectively. The varentropy of the inactivity time of a random variable is studied and termed by past varentropy in this paper. Reliability properties associated with the past varentropy and the reversed hazard rate function are discussed. Lower and upper bounds for the past varentropy are provided. The varentropy is applied for the proportional reversed hazard rate model. Also, asymptotic distribution for the information content of the inactivity time of a random variable is provided based on past entropy and varentropy.

Automated summary

The information content of a random variable is studied in the field of information theory. The mean and variance of the information content are referred to as entropy and varentropy, respectively. This paper focuses on the varentropy of the inactivity time of a random variable, termed as past varentropy. Reliability properties associated with the past varentropy and the reversed hazard rate function are discussed. Lower and upper bounds for the past varentropy are provided. The varentropy is applied to the proportional reversed hazard rate model. Furthermore, an asymptotic distribution for the information content of the inactivity time is derived based on past entropy and varentropy.