UJI GOODNESS OF FIT (GOF) DISTRIBUSI POPULASI BERDASARKAN STATISTIK BERBENTUK FUNGSIONAL DARI JEMBATAN BROWN

The purpose of this research is to derive Goodness of Fit (GoF) procedure for testing probability distribution model of a population based on a random sample taken from the population. The test statistics is a Cramér-Von Mises type statistics defined as a distance between the empirical distribution function of the sample and the distribution function of the population. Firstly, it is investigated that by applying multivariate central limit theorem, the empirical process converges to the Brownian briges. Next, by using continuous mapping theorem in metric space it is shown that the Cramér-Von Mises statistics converges to a statistics which is represented as an integral function of the quadtratic of the Brownian bridges. The rejection and acceptance regions of the test are determined by means of numerical approximation and Monte Carlo simulation methods. Both methods are shown to result in almost the same values of quantiles. The applications of the Cramér-Von Mises method to gold content data in Bombana as well as the Mercer-Hall (1911) data which is wheat yield on regular lattice design show that the probability distribution model of the populations from which the samples were drawn are normal.