Difficulties Involved in the Estimation of a Population Mean Using Transformed Sample Data

摘要: A problem of frequent occurrence in the statistical analysis experimental data is estimation first two moments a population with continuous but unknown c.d.f. F(x), based on random sample (x , * xn) - (x,). Standard estimates for E(x) and Var (x) are x or ?- t,_as/ n s respectively. If {x} non-normal S2 not minimum variance. For sake obtaining efficient var (xi) often transformed by function F: xi --, y, = F(xi)*, where F chosen so that (y,) satisfies tests normality. Estimates E(y) (y) then computed as y ?t tl-,s,/s/ s2 (It assumed such efficient; they are, fact sufficient provided we know {y} normal). Since these sufficient, them alone an estimate function's expected value. rule therefore commonly given estimating F-(y) (1)