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We introduce the transmuted modified Inverse Rayleigh distribution by using quadratic rank transmutation map (QRTM), which extends the modified Inverse Rayleigh distribution. A comprehensive account of the mathematical properties of the transmuted modified Inverse Rayleigh distribution are discussed. We derive the quantile, moments, moment generating function, entropy, mean deviation, Bonferroni and Lorenz curves, order statistics and maximum likelihood estimation The usefulness of the new model is illustrated using real lifetime data.