Transmuted inverse unit Teissier distribution: Properties, estimations and applications to medical and radiation sciences

The efficiency of probability distributions, which are fundamental to statistical analysis in many domains, is directly related to how well they match particular data attributes. Nonetheless, several real-world facts cast doubt on the presumptions of conventional distributions, highlighting the need for continuous improvements in probabilistic modeling. Anew, adaptable two-parameter modification of the inverse unit Teissier distribution (IUTD) developed using the transmutation approach is presented in this paper and called the transmuted inverse unit Teissier distribution (TrIUTD). By adding a transmutation parameter, the TrIUTD is better able to represent intricate data patterns that conventional distributions might not be able to fully represent. Because the TrIUTD's probability density function is right-skewed and unimodal, it can be used in a variety of contexts, including economic modeling, survival analysis, and reliability engineering. A growing failure rate is revealed by its hazard function, which makes it suitable for lifetime data analysis. The TrIUTD's quantile function, moments, survival function, odds ratio, failure rate average, Mills ratio, and order statistics were among its important attributes that were carefully deduced. Maximum likelihood estimation was shown to be the most reliable method out of fifteen various approaches used to estimate parameters for this model. Applications to three real-world datasets from the medical and radiation sciences proved the model's performance, and simulation tests verified the estimators' dependability. According to goodness-of-fit criteria, the TrIUTD showed abetter fit than well-known distributions, indicating its potential as a useful supplement to practical statistical modeling and distributional theory.