THE PROBABILITY INTEGRAL TRANSFORMATION FOR TESTING GOODNESS OF FIT AND COMBINING INDEPENDENT TESTS OF SIGNIFICANCE

摘要: y is a non-decreasing function of x, having values confined to the interval (0, 1). Further d p(y) = p(x)Iy I for < l. . (3) ~!dx In other words probability law integral, y, rectangular, all between O and 1 being equally likely occur. It follows that if we wish use set n independent observations x1, X2, ... X., test hypothesis Ho specified form, say p(x Ho), it may be possible carry out this by testing equivalent hypothesis, ho, corresponding YI, Y2, ..., Y,,, obtained means transformation (2), have been randomly drawn from rectangular distribution (3). The relation xi yi illustrated in Fig. 1; abscissae xi, (i 1, 2, .. ., 10), ten ordinates above, are shown below on scale 0 1. x's random sample population represented frequency curve therefore ho y's form distribution, range If laws p(x) not same x's, so