In this paper, we propose a new lifetime distribution with flexibility in modeling than its parent distribution. The new distribution is a variant of the Rama distribution having a positive shift parameter. We call the proposed distribution Shifted Rama (SR) distribution. Mathematical and statistical characteristics such as crude moments, central moment, coefficient of variation, index of dispersion, conditional moment, mean residual life function, mean deviation, Bonferroni and Lorenz curve, and the order statistics are derived. Furthermore, reliability measures like survival function, hazard function have been derived. Estimation techniques namely; the maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramer-von-Mises, Anderson-Darling and the right-tailed Anderson-Darling estimations are used. To demonstrate the applicability of the distribution, a numerical example was the blood cancer data from Ministry Hospital in Saudi Arabia. Based on the results, the proposed distribution performed better than the competing distributions. Simulation of the Estimates of the parameters based on the classical methods considered are obtained, and result showed that the maximum likelihood estimator gave the best classical estimates of the parameters compared to other methods considered.