- AndersonT. W. (1984). An Introduction to Multivariate Statistical Analysis, Second Edition, Wiley, New York.
- AndersonT. W., Das GuptaS. and StyanG. P. H. (1972). A Bibliography of Multivariate Statistical Analysis, Oliver & Boyd, Edinburg.
- Bagaio. P. (1960). Ph. D. Thesis, U. B. C., Vancouver, Canada.
- BagaiO. P. (1972). On the exact distribution of some p-variate test statistics with use of G-function, Sankhyā A, 34, 171–186.
- Bagaio. P. (1972a). On the exact distribution of a test statistic in multivariate analysis of variance, Sankhyā A, 34, 187–190.
- BartlettM. S. (1937). Properties of sufficiency and statistical tests, Proceedings of the Royal Statistical Society A, 160, 268–282.
- BasuA. P. (1969). On some tests for several linear relations. Journal of the Royal Statistical Society Series B, 31, 65–71.
- BraaksmaB. L. J. (1964). Asymptotic expansions and analytic continuations for Barnes' Integrals, Compositio Mathematica, 15, 239–341.
- CarterE. M., KhatriC. G. and SrivastavaM. S. (1976). On null distribution of likelihood ratio criterion for reality of covariance matrix, Journal of Multivariate Analysis, 6, 176–184.
- ChaoM. and GlaserR. E. (1978). The exact distribution of Bartlett's test statistics for homogeneity of variances with unequal sample sizes, Journal of the American Statistical Association, 73, 422–426.
- ConsulP. C. (1966). On the exact distribution of likelihood ratio criteria for testing linear hypotheses about regression coefficients, Annals of Mathematical Statistics, 37, 1319–1330.
- ConsulP. C. (1967). On the exact distributions of likelihood ratio criteria for testing independence of sets of variates under the null hypothesis, Annals of Mathematical Statistics, 38, 1160–1169.
- ConsulP. C. (1969). The exact distributions of likelihood ratio criteria for different hypothesis, Multivariate Analysis II, 171–181.
- CordeiroJ. A. (1980). Distribuições Exatas de Testes de Hipóteses Multivariada, Ph. D. Thesis, IMECC, Unicamp, CampinasBrazil.
- ErdélyiA., MagnusW. OberhettingerF. and TricomiF. G. (1953). Higher Transcendental Functions, Voi I, McGraw–Hill, New York.
- ExtonH. (1976). Multiple Hypergeometric Functions and Applications, Ellis Horwood Ltd., England.
- FoxC. (1961). The G and H-functions as symmetrical Fourier kernels, Transactions of the American Mathematical Society, 98, 395–429.
- GuptaA. K. (1973). On a test for reality of the covariance matrix in a complex Gaussian distribution, Journal of Statistical Computation and Simulation, 2, 333–342.
- GuptaA. K. and RathieA. K. (1982). Exact distribution of a LRC for the problems of k-samples, Metron, 40, 147–156.
- GuptaA. K. and RathieP. N. (1983). Non-null distribution of Wilks' λ in the complex linear case, Statistica, 43, 445–450.
- JainS. K., RathieP. N. and ShahM. C. (1975). The exact distributions of certain likelihood ratio criteria, Sankhyā A, 37, 150–163.
- JohnsonN. L. and KotzS. (1972). Distributions in Statistics: Continuous Multivariate Distributions, Wiley, New York.
- KabeD. G. (1958). Some applications of Meijer's G-functions to distribution problems in Statistics, Biometrika, 45, 578–580.
- KhatriC. G. (1965). A test of reality of a covariance matrix in a certain complex Gaussian distribution, Annals of Mathematical Statistics, 36, 115–119.
- KhatriC. G. (1965a). Classical statistical analysis based on a certain multivariate complex Gaussian distribution, Annals of Mathematical Statistics, 36, 98–114.
- KhatriC. G. and SrivastavaM. S. (1971). On exact non-null distributions of likelihood ratio criteria for sphericity test and equality of two covariance matrices, Sankhyā A, 33, 201–206.
- KotzS. and JohnsonN. L. (1982–1986). Encyclopedia of Statistical Sciences, Vol. 1 to 7, Wiley.
- KrishnaiahP. R. (1976). Some recent developments on complex multivariate distributions, Journal of Multivariate Analysis, 6, 1–30.
- KrishnaiahP. R. (1978). Some recent developments on real multivariate distributions, Development in Statistics, Vol I, (Ed. KrishnaiahP. R.), Academic Press, 135–169.
- LovettJ. N. (1977). Evaluation of the H-function inversion integral, Institute of Mathematical Statistics Bulletin, 6, 92.
- LukeY. L. (1969). The Special Functions and Their Approximations, Vol I & II, Academic Press, New York.
- LukeY. L. (1977). Algorithms for the Computation of Mathematical Functions, Academic Press, New York.
- MathaiA. M. (1970). Statistical theory of distributions and Meijer's G–function, Metron, 28, 122–146.
- MathaiA. M. (1970a). The exact distribution of a criterion for testing the hypothesis that several populations are identical, Journal of the Indian Statistical Association, 8, 1–17.
- MathaiA. M. (1970b). An expansion of Meijer's G–function in the logarithmic case with applications, Mathematische Nachrichten, 48, 129–139.
- MathaiA. M. (1970c). The exact distribution of Bartlett's criteria, Publi. L' ISUP, Paris, 19, 1–15.
- MathaiA. M. (1970d). Applications of Generalized Special Functions in Statistics, Research Monograph, McGill University and Indian Statistical Institute.
- MathaiA. M. (1971). On the distribution of the likelihood ratio criterion for testing linear hypothesis on regression coefficients, Annals of the Institute of Statistical Mathematics, 23, 181–197.
- MathaiA. M. (1972). Exact distribution of a criterion for testing equality of diagonal elements given that the covariance matrix is diagonal, Trabajos de Estadistica, 23, 67–83.
- MathaiA. M. (1972a). The exact distribution of a criterion for testing the hypothesis that a covariance matrix is diagonal, Trabajos de Estadistica, 23, 111–124.
- MathaiA. M. (1973). A review of the various methods of obtaining the exact distributions of multivariate test criteria, Sankhyā A, 35, 39–60.
- MathaiA. M. (1973a). A few remarks on some recent articles on the exact distributions of multivariate test criteria, Annals of the Institute of Statistical Mathematics, 25, 557–566.
- MathaiA. M. (1973b). A few remarks on the exact distributions of certain multivariate statistics-II, Proceedings of the Symposium on Multivariate Analysis, Hal-fix, 169–181.
- MathaiA. M. (1978). On the non-null distribution of Wilks' Lmvc, Sankhyā B, 40, 43–48.
- MathaiA. M. (1979). The exact distribution and the exact percentage points for testing equality of variances in independent normal populations, Journal of Statistical Computation and Simulation, 9, 169–182.
- MathaiA. M. (1979a). On the non-null distribution of test statistics connected with exponential populations, Communciations in Statistics. Theory and Methods, A 8 (1), 47–55.
- MathaiA. M. (1985). Exact and asymptotic procedures in the distribution of multivariate test statistics, Statistical Theory and Data Analysis, North-Holi and, 381–418.
- MathaiA. M. and KatiyarR. S. (1979). The distribution and the exact percentage points for Wilks' Lmvc criterion, Annals of the Institute of Statistical Mathematics, 31, 215–224.
- MathaiA. M. and KatiyarR. S. (1979a). Exact percentage points for testing independence, Biometrika, 66, 353–356.
- MathaiA. M. and KatiyarR. S. (1980). Exact percentage points for three tests associated with exponential populations, Sankhyā B, 42, 33–41.
- MathaiA. M. and RathieP. N. (1970). The exact distribution for the sphericity test, Journal of Statistical Research, 4, 140–159.
- MathaiA. M. and RathieP. N. (1970a). An expansion of G-function and its application to statistical problems, Bulletin de l'Academie royle de Belgique (Classe des Sciences), 56, 1073–1084.
- MathaiA. M. and RathieP. N. (1970b). The exact distribution of Votaw's criteria, Annals of the Institute of Statistical Mathematics, 22, 89–116.
- MathaiA. M. and RathieP. N. (1971). The problem of testing independence, Statistica, 31, 673–688.
- MathaiA. M. and RathieP. N. (1971a). The exact distribution of Wilks' criterion, Annals of Mathematical Statistics, 42, 1010–1019.
- MathaiA. M. and RathieP. N. (1980). On the non-null distribution of Wilks' Lvc criterion, Statistica, XL, 93–99.
- MathaiA. M. and RathieP. N. (1980a). On the non-null distribution of a test criterion for testing equality of populations, Multivariate Analysis V, 327–335.
- MathaiA. M. and RathieP. N. (1980b). The exact non-null distribution for testing equality of covariance matrices, Sankhyā A, 42, 78–87.
- MathaiA. M. and SaxenaR. K. (1973). Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer Verlag Lecture Notes Series in Mathematics, No. 348, New York.
- MathaiA. M. and SaxenaR. K. (1978). The H-function with Applications in Statistics and Other Disciplines, Wiley, New York.
- MathaiA. M. and TanW. Y. (1977). The non-null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix is diagonal, Canadian Journal of Statistics, 5, 63–74.
- MathaiA. M. and TracyD. S. (1985). Computable representations of a Mellin-Barnes integral through statistical techniques, Metron, 43, 117–126.
- MeijerC. S. (1946). On the G-function I – VIII, Nederlandse Akademie van Wetenschappen. Proceedings, 227–237; 344–356; 457–469; 632–641; 765–772; 936–943; 1063–1072; 1165–1175 (Indagationes Mathematicae 8, 124–134; 213–225; 312–324; 391–400; 468–475; 595–602; 661–670; 713–723).
- MellinH. J. (1910). Abrib einer einheitlichen theorie der gamma und der hyper– geometrischen funktionen, Mathematische Annalen, 68, 305–337.
- NagarD. K. (1985). The Exact Distributions of Certain Likelihood Ratio Test Criteria, Ph. D. Thesis, University of Rasjasthan, JaipurIndia.
- NagarsenkerB. N. (1975). The exact distribution of the LRC for testing equality of means, variances and covariances, Journal of Statistical Computation and Simulation, 4, 225–233.
- NagarsenkerB. and NagarsenkerP. B. (1982). Distributions of LRC associated with two-parameter exponential distributions, Communciations in Statistics. Theory and Methods, 11 (14), 1583–1593.
- NagarsenkerB. N. and PillaiK. C. S. (1973). Distribution of the likelihood ratio criterion for testing a hypothesis specifying a covariance matrix, Biometrika, 60, 359–364.
- NagarsenkerB. N. and PillaiK. C. S. (1974). Distribution of the likelihood ratio criterion for testing σ = σ0 μ = μ0 Journal of Multivariate Analysis, 4, 114–122.
- NairU. S. (1938). The application of the moment function in the study of distribution laws in Statistics, Biometrika, 30, 274–294.
- NandiS. B. (1980). On the exact distribution of normalized ratio of the weighted geometric mean to the unweighted arithmetic mean in samples from gamma distributions, Journal of the American Statistical Association, 75, 217–220.
- NandiS. B. (1981). The exact null distribution of Bartlett's criterion, Australian Journal of Statistics, 23, 45–51.
- NayakH. R. (1974). Generalized Hypergeometric Functions and Exact Distribution of Test Criteria, Master's Thesis, IIT BombayIndia.
- NeymanJ. and PearsonE. S. (1931). On the problems of K-samples, Bulletin de l'Academie Polonaise des Sciences, 3, 460–181.
- OliveiraN. F. de (1982). A Distribuiçā Exata de Criterio de Bartlett para Testar a Igualdade de Matriz da Covariancia, Master's Thesis, IMECC, Unicamp, CampinasBrazil.
- PearsonE. S. and WilksS. S. (1933). Methods of Statistical Analysis appropriate for k samples of two variables, Biometrika, 25, 353–378.
- PederzoliG and RathieA. K. (1983). The exact distribution of the LRC for testing independence of subvectors, Statistica, 43, 483–488.
- PederzoliG. and RathieP. N. (1983). The exact distribution of Bartlett's criterion for testing the equality of covariance matrices, Metron, 41, 83–89.
- PederzoliG. and RathieP. N. (1987). On the exact distribution of L1 (vc) of Votaw, Trabajos de Estadistica, 2, 79–87.
- PillaiK. C. S. (1956). On the distribution of the largest or the smallest root of a matrix in multivariate analysis, Biometrika, 43, 122–137.
- PillaiK. C. S. (1976). Distributions of characteristic roots in multivariate analysis: Part I: Null distributions, Canadian Journal of Statistics, 4, 157–184.
- PillaiK. C. S. (1977). Distributions of characteristic roots in multivariate analysis: Part II: Non-null distributions, Canadian Journal of Statistics, 5, 1–62.
- PillaiK. C. S., Al–AniS. and JourisG. M. (1969). On the distributions of the ratios of the roots of a covariance matrix and Wilks' criterion for tests of three hypotheses, Annals of Mathematical Statistics, 40, 2033–2040.
- PillaiK. C. S. and Nagarsenker (1972). On the distribution of a class of statistics in multivariate analysis, Journal of Multivariate Analysis, 2, 96–114.
- ProvostS. B. (1986). The exact distribution of the ratio of a linear combination of chi-square variables over the product of chi-square variates. Canadian Journal of Statistics, 14, 61–67.
- RaoC. R. (1972). Recent trends of research work in multivariate analysis, Biometrika, 28, 3–22.
- RathieA. K. (1980). A Study of H-function and Its Applications to Statistics, Ph. D. Thesis, University of Rajasthan, JaipurIndia.
- RathieN. R. (1981). Generalized Hypergeometric Functions and Statistical Distributions, Ph. D. Thesis, University of Rasjasthan, JaipurIndia.
- RathieN. R. (1982). On the exact distribution of Pearson and Wilks' likelihood test statistics, Metron, 40, 135–146.
- RathieN. R. (1983). The distribution of the LRC for testing a hypothesis on complex multivariate normal populations, Journal of Pure Applied Mathematics, 14, 1049–1055.
- RathieP. N. (1975). G-function and statistical distributions, Proc. 20th Brazilian Regional Conference of the International Biometrics Society, Piracicaba, S. P., September 1975, p. 432–441.
- RathieP. N. (1978). G and H–functions and statistical distributions, Metron, 36 (3–4), 141–149.
- RathieP. N. (1988). The exact distribution of a criterion for testing the hypothesis that several multivariate normal populations are identical, Statistica, Accepted for publication.
- RathieP. N. and RohrerH. G. (1988). The exact distribution of products of independent random variables, Metron, Accepted for publicaton.
- RathieP. N. and SrivastavaT. N. (1983). On the exact distribution of Votaw's criterion H1 (m), Metron, 41, 155–169.
- RoyJ. (1951). Distribution of certain likelihood ratio criteria useful in multivariate analysis, Proceedings of the International Statistical Congress, 219–230.
- SinghA. (1980). On the exact distribution of the likelihood ratio criterion for testing H : μ = μ0, σ = σ02I, Communications in Statistics. Simulation and Computation, B 9, 611–619.
- SinghA. (1982). Exact distribution of Wilks' Lvc criterion and its percentage points in the complex case, Communciations in Statistics. Simulation and Computation, 11, 217–225.
- SinghA. and PillaiK. C. S. (1983). On the exact non–null distribution of Wilks' Lvc criterion in the complex case, Sankhyā B, 45, 12–19.
- SpringerM. D. (1979). The Algebra of Random Variables, Wiley, New York.
- SrivastavaH. M., GuptaK. C. and GoyalS. P. (1982). The H–functions of One and Two Variables with Applications, South Asian Publishers Pvt. Ltd, New Delhi.
- SubrahmaniamK. and SubrahmaniamK. (1973). Multivariate Analysis : A Selected and Abstracted Bibliography, 1957–1972, Marcel Dekker, Inc., New York.
- SukhatmeP. V. (1936). On the analysis of K–samples from exponential populations with special reference to the problem of random interval statistics, Research Memoir, 1, 94.
- TitchmarshE. C. (1951). The Theory of the Riemann Zeta Function, Oxford University Press, London.
- VendraminiC. M. M. (1979). Distribuiçāo Exata do Criterio para Testar a Iqual–dade de Várias Distribuições Normais Multivariadas, Master's Thesis, Unicamp, CampinasBrazil.
- VotawD. F.Jr. (1948). Testing compound symmetry in normal multivariate distributions, Annals of Mathematical Statistics, 19, 447–473.
- WilksS. S. (1932). Certain generalizations in the analysis of variance, Biometrika, 24, 471–494.
- WilksS. S. (1934). Moment generating operators for determinants and product moments in samples from a normal system, Annals of Mathematical Statistics, 35, 312–340.
- WilksS. S. (1935). On the independence of k sets of normally distributed statistical variables, Econometrica, 3, 309–326.
- WilksS. S. (1946). Sample criteria for testing equality of means, equality of variances and equality of covariances in a normal multivariate distribution, Annals of Mathematical Statistics, 17, 257–281.
Generalized Hypergeometric Functions and Exact Distributions of Test Statistics
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.