The inverted Gompertz distribution,and some of its properties are investigated.  The distribution of the order statistic of the inverted Gompertz  distribution and some special cases are presented. Transformed distributions of this distribution are derived.  Based on Type II censored samples, the estimation of the shape and scale parameters, reliability and hazard rate functions are obtained using the maximum likelihood method. The uniformly minimum variance unbiased estimate of a function of the shape parameter is obtained assuming that the scale parameter is known. Asymptotic variances and covariances of the maximum likelihood estimators are found. Confidence intervals of the parameters are also given. Via a Monte Carlo simulation study, the estimated risks, squared bias and variances of the estimates are computed from different sample sizes.