In this work, we discuss constricting a mathematical formula based on a survival function. This formula has a basic parameter called a transmuted parameter. In addition, experimenting with this formula within Pareto distribution. The process of this production includes applying this formula to lifetime distributions. So the objective of this research is to formulate a distribution that is more flexible and accurate. A new model gives more accurate results on the application of data. The aim of the research study is to bring the transmuted survival Pareto distribution to closer to the Normal distribution. The probability density function, the probability cumulative function, and hazard function were extracted also, explaining the shapes of these functions for the model. Furthermore, derived the mathematical and statistical characteristics of the model. This model’s parameters are also estimated using a classical method (Maximum Likelihood estimation method).

Topics
Probability theory, Public and occupational health and safety, Estimation theory, Gaussian processes
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