χ2 test of goodness of fit for one-dimensional and multidimensional normal distribution, in specified case and unspecified case, with C++ source program

  • Authors:
  • Nicolae Popoviciu;Floarea Baicu

  • Affiliations:
  • Hyperion University of Bucharest, Faculty of Mathematics-Informatics, Bucharest, Romania;Hyperion University of Bucharest, Faculty of Mathematics-Informatics, Bucharest, Romania

  • Venue:
  • SEPADS'11 Proceedings of the 10th WSEAS international conference on Software engineering, parallel and distributed systems
  • Year:
  • 2011

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Abstract

The work has many sections. After a short description of χ2 test of goodness of fit (section 1), section 2 describes step by step two algorithms of χ2 test to verify the hypothesis of one-dimensional normal distribution: algorithm 1 in the specified case (m and σ2 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 χ2 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 χ2 test of multidimensional normal distribution in specified case and presents the algorithm AlgoHI2NormMultdSC. The section 5 deals with χ2 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 χ2 test for the algorithm 1. A Demo printed result is presented for this algorithm.