Assignment of frequencies to a completely ordered set of sample data

It is pointed out that the problem of reaching an optimum fit of a cumulative frequency curve by analytical methods does not involve directly the assignment of either individual confidence intervals or individual frequencies to the observed values of the sample. When one tests the nature of the function used to describe the behavior of the universe from which the sample be drawn, or the randomness of the observed sample, there may a rise the occasion for the assignment of individual confidence intervals to each sample value. The assignment of a best reference point (such as a best frequency value) within a confidence interval, such as the mean, median, or mode, is shown to be subordinate to that of the assignment of a confidence interval. If, for purposes of graphical fitting, it is found desirable to assign a frequency to each sample value, the writer, in general, recommends the mean frequency of the mth ordered observation: m = m/(n + 1) In certain cases it may be possible to estimate frequencies of the mth values by m = F[E(x m )] independently of the unknown parameters, and such points might prove more desirable to use for graphical fitting near the extremes, if errors along the x direction are balanced out visually, relative to these points.