Abstract
A random variableX is said to have a symmetric distribution (about 0) if and only ifX and −X are, identically distributed. By considering various types of partial orderings between the distributions ofX and −X, one obtains various notions of skewness or one-sided bias. In this paper we study likelihood ratio tests for testing the symmetry of a discrete distribution about zero against the alternatives, (i)X is stochastically greater than −X; and (ii) pr(X=j)≥pr(X=−j) for allj>0. In the process, we obtain maximum likelihood estimators of the distribution function under the above alternatives. The asymptotic null distributions of the test statistics have been obtained and are of the chi-bar square type. A simulation study was performed to compare the powers of these tests with other tests.
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Dykstra, R., Kochar, S. & Robertson, T. Likelihood ratio tests for symmetry against one-sided alternatives. Ann Inst Stat Math 47, 719–730 (1995). https://doi.org/10.1007/BF01856543
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DOI: https://doi.org/10.1007/BF01856543