Quadratic distance methods based on a special distance which make use of survival functions are developed for inferences for bivariate continuous models using selected points on the nonegative quadrant. A related version which can be viewed as a simulated version is also developed and appears to be suitable for bivariate distributions with no closed form expressions and numerically not tractable but it is easy to simulate from these distributions. The notion of an adaptive basis is introduced

more »

... d the estimators can be viewed as quasilikelihood estimators using the projected score functions on an adaptive basis and they are closely related to minimum chi-square estimators with random cells which can also be viewed as quasilikeliood estimators using a projected score functions on a special adaptive basis but the elements of such a basis were linearly dependent. A rule for selecting points on the nonnegative quadrant which make use of quasi Monte Carlo (QMC) numbers and two sample quantiles of the two marginal distributions is proposed if complete data is available and like minimum chi-square methods; the quadratic distance methods also offer chi-square statistics which appear to be useful in practice for model testing. Marshall and Olkin [3] (p. 840). Later on in section (1.2) we shall examine another way to create new survival functions. Unlike new distributions created using the BSPM operator, new distributions created using means of trivariate reduction techniques often do not even have an integral representation despite the functions used are simple for examples linear functions. We shall discuss further trivariate reduction techniques in section 1.2 and consider first a few examples of new distributions cretead using the BSPM operator subsequently. A. Luong