On the exact distribution of Votaw’s \(L_ 1(vc)\) criterion. (Spanish. English summary) Zbl 0731.62057
Summary: This paper deals with the exact distribution of \(L_ 1(vc)\) of D. F. Votaw [Ann. Math. Statist., Baltimore Md. 19, 447-473 (1948; Zbl 0033.079)]. The results are given in terms of Meijer’s G-function as well as in series form suitable for computation of percentage points.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62H10 | Multivariate distribution of statistics |
| 33C60 | Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) |
Keywords:
Votaw’s criterion; generalized hypergeometric functions; inverse Mellin transform; t-variate normal population; Meijer’s G-function; computation of percentage pointsCitations:
Zbl 0033.079References:
| [1] | ANDERSON, T. W. (1984):Introduction to Multivariate Statistical Analysis, Wiley, New York. · Zbl 0651.62041 |
| [2] | LUKE, Y. L. (1969):The Special Functions and Their Approximations, Vol. I, Academic Press, New York. · Zbl 0193.01701 |
| [3] | MATHAI, A. M. and RATHIE P. N. (1970): “The exact distribution of Votaw’s criteria{”,Ann. Inst. Statist. Math. 22, 89–116.} · Zbl 0218.62054 · doi:10.1007/BF02506326 |
| [4] | MATHAI, A. M. and RATHIE P. N. (1971): “The exact distribution of Wilks’ criterion{”,Ann. Math. Statist., 42, 1010–1019.} · Zbl 0216.21805 · doi:10.1214/aoms/1177693329 |
| [5] | PEDERZOLI, G. and RATHIE, P. N. (1983): “The exact distribution of Bartlett’s criterion for testing the equality of covariance matrices{”,Metron, Vol. XLI, No. 3-4, 83–89.} · Zbl 0547.62035 |
| [6] | VOTAW, D. F. (1948): “Testing compound symmetry in normal multivariate distribution{”,Ann. Math. Statist., 19, 447–473.} · Zbl 0033.07903 · doi:10.1214/aoms/1177730145 |
| [7] | WILKS, S. S. (1982): “Certain Generalizations in the Analysis of Variance{”,Biometrika, 24, 471–494.} · Zbl 0006.02301 · doi:10.1093/biomet/24.3-4.471 |
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