Extremely deviating outcomes, in the sample are termed as outliers, they give faulty measures and the results in wrong directioned conclusions. The backbone of this work is based on the study of outliers, categorized here into Static and Dynamic models. Concerning the ’Static Statistical Distributions’, a novel approach for normally distributed data had been developed by J. W. Dixon in 1950’s. The first half of the study uses the same idea by arranging the data set in ascending order for the particular cases where samples are comming out of either • Uniform distribution, or • Exponential distribution. For the procedure of hypothesis testing, the percentage points have been constructed separately for both distributions. Comming towards the second half, ’the Dynamic models’, main concern of the study is on Box and Jenkin’s model. Additive white noise in time discrete differential equation as a special case of ARMA(p, q) model has been considered. The special form of variancecovariance matrix enable us to develop a new procedure for the detection of outlier while working with Poisson Process. The likelihood estimation, originally proposed by Fox (1972) has been used with the assumption of known autoregressive parameters. Through the characteristic function, the distribution of the test has been evaluated. For unknown autoregressive parameters, Yule-Walker and Whittle estimation procedures have been discussed briefly. ’Kalman Filtering’ recursive method opens broader ways for the parameter estimation as well as for outlier detection. Some supporting practical examples for the new test have also been discussed.