- Getachew Tekle: Department of Statistics, Wachemo University, Hossana, Ethiopia. getachewtekle@wcu.edu.et.
- Rasool Roozegar: Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran.
Methodological developments in different sectors like health, biomedical and biological areas are the recent burning issue in the statistical literature. The approach of implementing declining hazard function which is obtained by compounding truncated Poisson distribution and a lifetime distribution is a special concern in a few studies. In this paper we proposed a newly introduced distribution called inverse Lomax-Uniform Poisson distribution mostly applied in the health, biomedical, biological, and related sectors. Some basic statistical properties of the distribution are discussed. The capability of the model is checked by comparing it with six potential models by using a practical real data set. Based on the comparison techniques, the newly proposed model out performs all its counterparts. The simulation study is also conducted. Furthermore, the joint modelling of repeatedly measured and time-to-vent processes is discussed in detail with the real data set in the health sector.