Abstract
This paper offers the odd inverted Topp-Leone family of probability distributions with new statistical models capable of fitting data in various fields. Different density function shapes as well as different shapes of hazard rate are observed. Explicit formulas of structural properties to the family are discussed. The two-parameter inverted Topp-Leone exponential distribution, which has been created as part of the offered family, has been explored due to its intended features for the statistical modeling. Parameter estimation of the inverted Top-p-Leone exponential distribution is considered under complete and censored samples. The usefulness of the estimators is regarded by employing Monte Carlo simulations. We deal with practical data analysis for new modeling strategy, which gives quite convenient results compared with some other models.