A test for goodness of fit usually involves examining a random sample from some unknown distribution in order to test the null hypothesis that the unknown distribution function is in fact a known, specified function. The Chi-square test can be applied to any univariate distribution for which you can calculate the cumulative distribution function. The Chi-square test does not have good propertie...

The aim of this paper is to relate and extend some recent work on chi-square goodness-of-fit tests. There is no discussion of any problems which are specifically associated with more than one categorical variable.. The main topics are the effect of estimation on chi-square and its partitions ~~d their relation to Neymants smooth goodness-of-fit test, and the effect of grotp:ing a univariate dis...

For many probability laws, in parametric models, the estimation of parameters can be done frame maximum likelihood method, or moment methods, by using plug-in etc. Usually, for estimating more than one parameter, same is used. We focus on method this paper. use instrumental tool functional empirical process (fep) Lo (2016) to show how it practical derive, almost algebraically, joint distributio...