a three-parameter new discrete analog of Alpha-power Weibull distribution (DAPW) is presented. Some of its fundamental distributional and reliability properties are established. Two datasets are used showing the flexibility of the proposed model. An attempt to introduce a new lifetime model as a discrete version of the continuous exponentiated exponential distribution which is called discrete exponentiated exponential distribution (DEE). a discrete analog of the continuous generalized inverted exponential distribution denoted by discrete generalized inverted exponential distribution (DGIE). The model with two real data sets is also examined. In addition, the developed DGIE is applied as color image segmentation which aims to cluster the pixels into their groups. To evaluate the performance of DGIE, a set of six color images is used, as well as it is compared with other image segmentation methods including Gaussian mixture model (GMM), K-means, and Fuzzy subspace clustering (FSC). The DGIE provides high performance than other competitive methods.