Downloaded from https://www.everyspec.com AMCP 70U 196 C, arnd D piotted, repectively. onl lognormazl plotting value front Flq 2-4). The horizontal probability paper using thc K-S Bound& and vertical icales are, the same; No the pop- method. The . -onfideneo levels art the ulption (shown solid) plots as a 45-dog some as used for the same data sets in earlier straight hitc. Fig. 2-11I shows nil 9 order pitragraphs. See Instructions for use on the statistics tro'n it sample of 9. Again, ihle roverse side of the Practical Probabifly Paper. horizontal and vertical %cale% are the same, No the populition pluot as at 45-deg stradight Data Set A (Fig. 2-7) could reasonably line.
(The K-S bounds af0 not shown here haive come from a lognormal dlatributioui. iii this special case. so as not to clutter up The parameter estimateso, f'tom lines #1I - #5 the figures.) ame: All 3 Outa sets (A,C,I)) could reasonably or 1450 hr, 1900 hr, have conmc from aniy of thc 3 distributions: x-normal. Wuibull, or lopnormal. It is fruit- apv 2400 hr less to try to pick tho "boot" one: that would be an exerciso In slerife, pointless mathe- Data Set C (Fig. 2-8) could reasonaibly Before you p)ursue the questions uf' whtich have come fromt a lognormal distribution.
distrlbutions and what parameter valu~es, ask N~o parameter estimatotb were made because yourself "Why do I want to know?" II'it'u they wuuld serve little purpose, The reason because you wan~t to estimato some property Data Sol C could reasionably have conic, lronm of the population. otopi Youi're kidding u lognormal distribution Is that it varioty ofI yourself if you think mathematical manipula- straight lines could be drawn within the K-S tiouis will tell you thie answer when the graph envelope in Fig. 2-8. Anyone of thiose lines says yous don't know, ,ould be the actual distribution, D~o not try to estimate a location piaram- Data Set D (Fig.
2-9) could reasonably oetr for Weibufl iisid lognormal difltrihotioni have come from a logniormal distribution. by "rIng to "straighten-out" the samnple plot. No parameter ostimateui were maide, If you are over tempted to do it, look uyniiu - at Figs. 2-1(0 and 2-11 WI wiCfhhow hlow-IM, Small samples (e.g., 20 ot less) cannot pill. ly-picol" it random saimple usually it., point the distribution from wihence they came. Lognormal and Weibuli distributions (iraphilval estimation usually Call Provide arm difficult to tell upart eveni with somewhat all the accuracy that the datat calt use, It Iarpr samples.
call give u good picture or' the uncertainty in any extrapolation (or interpolation) from 2-2.6 SUMMARY the samiple. It call also make you think harder about why you wanted to estimate Small samples (say, less than 20) ure floto- some parameters fronti the data. When an riously unreliable indicators for the shape of Iterative analytic miethod Is used to estimate a population. Always plot the K-S bounds l.arainefers, the graphicul esimates are usu- along with the sample Cdf. Figs. 21-10 and ally vxcellent Owievs, Cor the starting point, 2-1 1 sllow the behavior of samples from the uniform distribution (see Ref. 27). Fig. 2-10 Beware.
of' ilafa froin small samples that shows the first 10 order statistics out of a plot its very straight line% on tiny kind of sample of 99 (the plots are vs the moan prohailliiity papet, Thie ciatiwes of its hiap" li xt contifmes onU ~page .1-4 -. 2.~~~736.......... . . . . ... w.. . .