Analysis of kidney patients and pump failure data using a new unit interval distribution

A new one-parameter unit model is developed and investigated. The new model is known as the unit moment exponential distribution. Some essential mathematical characteristics of the distribution are determined. The model parameter is estimated using five distinct estimation approaches, including maximum likelihood, Anderson Darling, Cramer-von Mises, Ordinary least squares, and weighted least squares. A detailed simulation study is used to evaluate the behavior of engendered estimators. Maximum likelihood approaches appear to be an effective estimation technique. A regression model based on a new distribution is also derived. The validity and applicability of the new distribution are evaluated using two datasets, one on the duration of renal dialysis and the other on pump failure. It is identified that the new model efficiently analyzes these considered datasets.