Estimation of Population Mean under logarithmic for the Poisson Distributed Study and Auxiliary Variates

: Use of suitable auxiliary information is always suggested in literature at the planning and estimation stage to make the estimators more powerful in terms of efficiency. Estimation using auxiliary information is common in sampling literature but using distribution of study and auxiliary information at the estimation stage is uncommon and useful specially when dealing with rare variable. This study utilizes the auxiliary information and Poisson distributed variates for proposing the log-type estimator and another generalized estimator for finite population mean under simple random sampling without replacement. The Mean Square Error expressions of the proposed estimators are obtained and mathematical conditions are established to prove the efficiency of proposed estimators.  It is revealed from empirical (point estimation and interval estimation) & theoretical study that use of log type estimators along with suitable auxiliary information for Poisson distributed variates excels the performance of estimators in terms of efficiency.