Statistical Estimation

Abstract

There are practical situations where one would like to estimate some parameters of an underlying statistical distribution. For example, a toothpaste manufacturer would like to make a statement such as his new toothpaste would reduce cavities by 21 to 49%. Here the manufacturer is interested in two numbers such as 21% and 49% such that the true proportion of reduction in cavities is somewhere between 21% and 49%. A weather bureau may forecast the temperature variation in a forthcoming month as between a°F and b°F and it may claim that, the forecast will be correct in 95% of the cases. A design engineer would like to get an estimate of the average weight of the type of passengers who are likely to fly, when designing an aircraft. In all these problems one would like to get an estimate of an unknown quantity. In statistical estimation problems, one is interested in getting an estimate of either an unknown parameter or an unknown probability-statement. Two types of estimates for a parameter are usually sought for. They are the point estimates and the interval estimates.