Geodesic
On testing the symmetry of distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 372-377

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Let $F(x)$ be an unknown distribution function. The hypothesis to be tested is the symmetry of $F(x)$ at $x=0\colon F(-x)=1-F(x)$. A test of the $\omega^2$-test type is constructed, and its asymptotic properties are investigated. 
@article{TVP_1972_17_2_a15,
     author = {A. I. Orlov},
     title = {On testing the symmetry of distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {372--377},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a15/}
}
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A. I. Orlov. On testing the symmetry of distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 372-377. http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a15/