The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp-Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp-Leone (TPITL) distribution. The power inverted Topp-Leone and the inverted Topp-Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp-Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.
Keywords: maximum product spacing; power inverted Topp–Leone distribution; stochastic ordering; transmuted family.