Geodesic
Limit distributions of the Pearson statistics for nonhomogeneous polynomial scheme
Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 121-129

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For a nonhomogeneous polynomial scheme, conditions are found under which the Pearson statistic distributions converge to the distribution of nonnegative quadratic form of independent random variables with the standard normal distribution.
Keywords: chi-square test, Pearson statistics, limit distributions, noncentral weighted chi-square distribution. 
@article{DM_2017_29_4_a7,
     author = {M. P. Savelov},
     title = {Limit distributions of the {Pearson} statistics for nonhomogeneous polynomial scheme},
     journal = {Diskretnaya Matematika},
     pages = {121--129},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_4_a7/}
}
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M. P. Savelov. Limit distributions of the Pearson statistics for nonhomogeneous polynomial scheme. Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 121-129. http://geodesic.mathdoc.fr/item/DM_2017_29_4_a7/