x~2 Test of Goodness of Fit for One-dimensional and Multidimensional Normal Distribution, in Specified Case and Unspecified Case, with C++ Source Program

摘要

The work has many sections. After a short description of x~2 test of goodness of fit (section 1), section 2 describes step by step two algorithms of x~2 test to verify the hypothesis of one-dimensional normal distribution: algorithm 1 in the specified case (m and σ~2 are known values) and algorithm 2 in the unspecified case (m* and σ~*2 are estimated values). Both algorithms are validated by simulated data. The section 3 gives the algorithm 3 for x~2 test of log-normal distribution in unspecified case. The log-normal distribution is appropriate for estimation of reliability parameters for semiconductor devices. The application of algorithm 3 is the aim of [6], where experimental data are used. The log-normal hypothesis H is accepted. The section 4 deals with x~2 test of multidimensional normal distribution in specified case and presents the algorithm AlgoHI2NormMultdSC. The section 5 deals with x~2 test of multidimensional normal distribution in unspecified case and presents the algorithm AlgoHI2NormMultdUSC. The last two algorithms are validated by numerical data. The section 6 contains a C++ source program of x~2 test for the algorithm 1. A Demo printed result is presented for this algorithm.