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In practice, the use of rounding is ubiquitous. Although researchers havelooked at the implications of rounding continuous random variables, roundingmay be applied to functions of discrete random variables as well. For example,to infer on suicide excess deaths after a national emergency, authorities mayprovide a rounded average of deaths before and after the emergency started.Suicide rates tend to be relatively low around the world and such rounding mayseriously affect inference on the change of suicide rate. In this paper, westudy the scenario when a rounded to nearest integer average is used as a proxyfor a non-negative discrete random variable. Specifically, our interest is indrawing inference on a parameter from the pmf of Y , when we get U = n[Y /n] asa proxy for Y . The probability generating function of U , E(U ), and Var(U )capture the effect of the coarsening of the support of Y . Also, moments andestimators of distribution parameters are explored for some special cases. Weshow that under certain conditions, there is little impact from rounding.However, we also find scenarios where rounding can significantly affectstatistical inference as demonstrated in three examples. The simple methods wepropose are able to partially counter rounding error effects. While for someprobability distributions it may be difficult to derive maximum likelihoodestimators as a function of U , we provide a framework to obtain an estimatornumerically.

Estimating Counts Through an Average Rounded to the Nearest Non-negative Integer and its Theoretical & Practical Effects