We propose a two parameter Inverted Generalized Exponential (IGE) and a three parameter Generalized Inverted
Generalized Exponential (GIGE) probability models as generalizations of the one-parameter Exponential distribution and some other
distributions in the literature. We explore the statistical properties of the GIGE distribution and its parameters were estimated for both
censored and uncensored cases using the method of maximum likelihood estimation (MLE). An application to a real data set is also
provided to assess the flexibility of the GIGE distribution over some of its sub-models