Another look at plotting positions

Abstract

Probability paper was used as early as 1896, and was mentioned in the literature more than 30 times before 1950, mainly by hydrologists, most of whom used the plotting position (i-0.5)/n proposed by Hazen (1914). Gumbel (1942a) considered the modal position (i-1)/(n-1) and the mean position i/(n+1) [the latter proposed by Weibull (1939a,b)], and chose the latter. Lebedev (1952) and others proposed the use of (i-0.3)/(n+0.4), which is approximately the median position advocated by Johnson (1951). Blom (1958) sug-gested (i-α)/(n-2α+1), where a is a constant (usually 0 ≤ α ≤ 1), which includes all of the above plotting positions as special cases. Moreover, by proper choice of α, one can approximate F[E(xi)], the position proposed by Kimball (1946), for any distri-bution of interest. Gumbel (1954) stated five postulates which plotting positions should satisfy. Chernoff & Lieberman (1954) discussed the optimum choice of plotting positions in various situ-ations. It is clear that the optimum plotting position depends on the use that is to be made of the results and may also depend on the underlying distribution. The author endeavors to formulate recommendations as to the best choice in various situations.