In this article, a new distribution for count data analysis is introduced. Firstly, the Discrete Transmuted Generalized Inverse Weibull distribution (DTGIW) is constructed. Consequently, some useful sub-models are discussed. Secondly, the ZeroTruncated Discrete Transmuted Generalized Inverse Weibull distribution (ZT-DTGIW) is introduced. We present probability mass function of the proposed distribution and some plots of those functions for illustration the behaviors of the distribution. We employed the maximum likelihood estimation (MLE) technique for model parameter estimation. For the purpose of verification of the MLE performance, the simulation study of parameter estimation using MLE is illustrated. Finally, some real data sets are applied to illustrate the goodness of fit of the proposed distribution, which is compared with the zero-truncated discrete inverse Weibull and zero-truncated Poisson distributions.
