No abstract

No abstract

No abstract

SuniinaryDensities, citniultitives, and qita~itilcs of the noncentral distributions nre notoriously difficult to cnlculate. I t is shown how the noncentral t distribution is represented in the canonical S-systciii form, i.e., as a set of first-order nonlinear differential equations in which the derivative of each variable equals a difference of two products of power-law functions. By solving the S-system numerimlly one rapidly obtains densitiea, cumulativea, quantiles, and moments of thc ccntr:iI crnd noncentrel 1 distributions, ~8 well aa power functions for the I-test. These are quite extensive, but it is obvious that not every possible choice of alevels, degrees of freedom, or noncentrality parameters can be provided, and often one has to estimate the desired quantity through interpolation.