In this article, we will study the estimation of the unknown parameters for exponentiated gamma distribution as well as a survival function, failure rate function and the coefficient of variation based on unified hybrid censored data. In addition that, we will study maximum likelihood and Bayesian estimates. To calculate the Bayes estimates of the model parameters  will beused Markov chain Monte Carlo method (MCMC). Gibbs within the Metropolis-Hasting algorithm has been applied to generate MCMC samples from the posterior density function and calculate approximate confidence intervals for the unknown parameters, survival, failure rate functions and coefficient of variation. All resultsobtained are based on the balanced-squared error loss, balanced linear-exponential loss, and balanced general entropy loss functions. At the end of article, real data has been used to determine how the estimation method can be used in practice.