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Let us denote p(x|K) the space density of the points where identicalparticles of some kind, e.g. pi+ mesons, with momentum K are produced. Whenusing the HBT method to determine p(x|K) one encounters ambiguities. We showthat these ambiguities do not affect the even cumulants of the distributionp(x|K). In particular, the HBT radii of the homogeneity regions, which aregiven by the second order cumulants, and the distribution of distances betweenthe pairs of production points for particles with momentum K can be reliablymeasured. The odd cumulants are ambiguous. The are, however, correlated. Inparticular, when the average position <x>(K) is known as a function of K thereis no further ambiguity.

Use of cumulants to quantify uncertainties in the HBT measurements of the homogeneity regions