A Distribution-Free Test for Symmetry Based on a Runs Statistic

McWilliams, Thomas P.

doi:10.1080/01621459.1990.10474985

Cited by 68 publications

(75 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…P(T 1,n = 1) = P(−X (2) < X (1) < −X (1) ) = P(F(X (1) ) < F(−X (1) )) − P(F(X (1) ) < F(−X (2) )) = P(U (1) ) < 0.5) − P(U (1) + U (2) < 1) = P(X (1) < −X (t) ) − P(X (1) < −X (t+1) ) = P(F(X (1) ) < F(−X (t) )) − P(F(X (1) ) < F(−X (t+1) )) = P(U (1) + U (t) < 1) − P(U (1) + U (t+1) < 1) = P(X (i) < −X (t) ) − P(X (i) < −X (t+1) ) = P(F(X (i) ) < F(−X (t) )) − P(F(X (i) ) < F(−X (t+1) )) = P(U (i) + U (t) < 1) − P(U (i) + U (t+1) < 1) = P(X (i) < −X (i−1) ) − P(X (i) < −X (i) ) = P(F(X (i) ) < F(−X (i−1) )) − P(F(X (i) ) < F(−X (i) )) = P(U (i−1) + U (i) < 1) − P(U (i) < 0.5) = P(X (i) < −X (i) ) − P(X (i) < −X (i+1) ) = P(F(X (i) ) < F(−X (i) )) − P(F(X (i) ) < F(−X (i+1) )) = P(U (i) < 0.5) − P(U (i) + U (i+1) < 1) and P(T i,n = t) = P(−X (t+1) < X (i) < −X (t) ) = P(X (i) < −X (t) ) − P(X (i) < −X (t+1) ) = P(F(X (i) ) < F(−X (t) )) − P(F(X (i) ) < F(−X (t+1) )) = P(X (n) < −X (t) ) − P(X (n) < −X (t+1) ) = P(F(X (n) ) < F(−X (t) )) − P(F(X (n) ) < F(−X (t+1) )) = P(U (n) + U (t) < 1) − P(U (n) + U (t+1) < 1)…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A new test for symmetry against right skewness

Amiri

Khaledi

2015

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

Let X be a continuous random variable with distribution function F. If F is symmetric about 0, then for 0 < p < 1, η p = −η 1−p , where η p is the pth quantile of X. Using this well-known observation, based on a random sample from F, a new test of symmetry against right skewness is proposed and its exact null distribution is obtained. It is shown that the proposed test is relatively more powerful than some other tests in the literature including a test given by Corzo and Babativa [A modified runs test for symmetry. J Statist Comput Simul. 2013; 83: 984-991].

show abstract

Section: Resultsmentioning

confidence: 99%

“…. , X n be a random sample from an absolutely continuous distribution F with median zero and X (1) , . .…”

Section: Introduction and Proposed Testmentioning

confidence: 99%

A new test for symmetry against right skewness

Amiri

Khaledi

2015

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

show abstract

“…, I n weighted according to their positions. A critical region for the J k test can be built following the argument of McWilliams [1], which establishes that under asymmetry of F and, for b > a > 0, either…”

Section: The Modified Testmentioning

confidence: 99%

“…This test problem has received considerable attention in the literature; see, for example [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A modified runs test for symmetry

Corzo

Babativa

2013

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

We propose a modification of a Modarres-Gastwirth test for the hypothesis of symmetry about a known center. By means of a Monte Carlo Study we show that the modified test overtakes the original ModarresGastwirth test for a wide spectrum of asymmetrical alternatives coming from the lambda family and for all assayed sample sizes. We also show that our test is the best runs test among the runs tests we have compared.

show abstract

“…Each adaptive procedure uses in its first stage some measure or test of symmetry to decide whether the W + test or the S + test should be used to test the hypothesis about the median of the distribution. The first test (R) is based on calculating the runs statistic of symmetry [5]. A disadvantage with the procedure is that the runs test may give highly significant values, not because the distribution is asymmetric but because it is symmetric about the true value of the median which is different from the one specified by the null hypothesis.…”

Section: Introductionmentioning

confidence: 99%