Zero-inflated count models provide a method to explain the excess zeros by modeling the data as a mixture of two separate distributions: one distribution is typically a Poisson or negative binomial distribution that can generate both zero and nonzero counts, and the second distribution is a constant distribution that generates only zero counts. Standard discrete distribution may fail to fit such data either because of zero inflation or over/under dispersion. Now, there is increased interest in a zero inflated distribution to account for extra zeros in data. Failure to account for extra zeros may result in biased parameter estimates and misleading inference. Because the zero inflated distributions usually provide better statistical fit. These types of data are commonly found in various scientific disciplines such as biomedical, econometrical, ecology, and health sciences. As mentioned above, the mixed distribution defines one of the most important ways to obtain a new probability distribution in applied probability and operational research. For the purpose, we are looking for a new zero inflated distribution which is a more flexible alternative to fit count data with excess zeros. When the underlying count distribution is a negative binomial, the mixture is called a zero inflated negative binomial (ZINB) distribution. ZINB models are better models to fit count data with excess zeros. Count data often show a higher incidence of zero counts than would be expected if the data were negative binomial distributed. For testing appropriate model to count data, can used the test such as Wald test, likelihood ratio test and score test. The score test has an advantage over the LRT and the Wald test in that the score test only requires the interested parameter be estimated under the null hypothesis. In this thesis, a score test presented for testing zero inflated negative Binomial against a negative binomial model and show that zero inflated negative binomial models fitted better for count data with excess zeros. Some simulation studies are conducted for different testing procedures and the likelihood of making a type I error and power of test are computed. The result of simulation show that, When the sample size increases, the probability of type I error was close to the nominal level of significance. Also, for small sample sizes, such as n = 5, 15, the score test is conservative. In order to do this test, point null hypothesis versus one sided hypothesis are considered concerning inflation parameter in zero inflated negative binomial distribution. When the sample size is small, asymptotic behavior of test statistic such as score test may be poor. So Bayesian test of detecting inflation is considered. Uniform and Jeffreys’ priors are used as a prior distribution of interested the parameters. Also Bayes factor is obtained as a measure of evidence. Some simulation studies are conducted for different testing procedures and the likelihood of making a type I error and power of test are computed for Two ltr"