Independence of the Residual Quadratic Sums in the Dispersion Equation with Noncentral χ^{2}-Distribution

ABSTRACT

A model adequacy test should be carried out on the basis of accurate aprioristic ideas about a class of adequate models, as in solving of practical problems this class is final. In article, the quadratic sums entering into the equation of the dispersive analysis are considered and their independence is proved. Necessary and sufficient conditions of existence of adequate models are resulted. It is shown that the class of adequate models is infinite.

A model adequacy test should be carried out on the basis of accurate aprioristic ideas about a class of adequate models, as in solving of practical problems this class is final. In article, the quadratic sums entering into the equation of the dispersive analysis are considered and their independence is proved. Necessary and sufficient conditions of existence of adequate models are resulted. It is shown that the class of adequate models is infinite.

Cite this paper

nullN. Sidnyaev and K. Andreytseva, "Independence of the Residual Quadratic Sums in the Dispersion Equation with Noncentral χ^{2}-Distribution," *Applied Mathematics*, Vol. 2 No. 10, 2011, pp. 1303-1308. doi: 10.4236/am.2011.210181.

nullN. Sidnyaev and K. Andreytseva, "Independence of the Residual Quadratic Sums in the Dispersion Equation with Noncentral χ

References

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[2] V. A. Kolemaev, O. V. Staroverov and A. S. Turundaevski, “The Probability Theory and Mathematical Statistics,” Vyishaya Shkola, Moscow, 1991, pp. 16-34.

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[4] N. I. Sidnyaev, V. A. Levin and N. E. Afonina, “Mathematical Modeling of Intensity of Heat Transmission by Means of the Theory of Planning an Experiment,” Inzhenerno Fizicheskii Gurnal (IFG), Vol. 75, No. 2, 2002, pp. 132-138.

[5] N. I. Sidnyaev, “The Theory of Planning Experiment and Analysis of Statistical Data,” URight, Moscow, 2011, pp. 95-220.

[1] V. S. Asaturyan, “The Theory of Planning an Experi-ment,” Radio I Svyaz, Vol. 73, No. 3, 1983, pp. 35-241.

[2] V. A. Kolemaev, O. V. Staroverov and A. S. Turundaevski, “The Probability Theory and Mathematical Statistics,” Vyishaya Shkola, Moscow, 1991, pp. 16-34.

[3] O. I. Teskin, “Statistical Processing and Planning an Experiment,” MVTU, Moscow, 1982, pp. 12-26.

[4] N. I. Sidnyaev, V. A. Levin and N. E. Afonina, “Mathematical Modeling of Intensity of Heat Transmission by Means of the Theory of Planning an Experiment,” Inzhenerno Fizicheskii Gurnal (IFG), Vol. 75, No. 2, 2002, pp. 132-138.

[5] N. I. Sidnyaev, “The Theory of Planning Experiment and Analysis of Statistical Data,” URight, Moscow, 2011, pp. 95-220.