The Quadratic rank transmutation map was proposed and studied for introducing skewness and flexibility into probability models with a single parameter known as the transmuted parameter. This methodology has received greater attention and application using several classical distributions however, the Exponential Inverse Exponential distribution has not been transmuted since its introduction. This article uses this method to add flexibility to the Exponential Inverse Exponential distribution which results to a new continuous distribution called Transmuted Exponential Inverse Exponential distribution. This paper presents the definition, validation, properties, applications and estimation of unknown parameters of the transmuted Exponential Inverse Exponential distribution using the method of maximum likelihood estimation. The new distribution has been applied to three real life datasets and results provide evidence that it is better than the other existing distributions based on the datasets used. Thus, this new model can be applied fully in modeling real life problems most especially in survival analysis.
Key words: Quadratic Rank Transmutation Map, Transmuted Exponential Inverse Exponential Distribution, Definition, Validity, Properties, Maximum Likelihood Estimation, Applications. Survival Analysis.
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