Distributions on the Simplex for the Analysis of Neutrality

The useful independence concept of neutrality introduced by Connor and Mosimann (1969) for the analysis of proportions has not yet been fully exploited because of the lack of a rich parametric class of distributions on the simplex which will accomodate both neutrality and non-neutrality. This paper provides such a class of distributions and so opens the way to standard statistical tests of neutrality hypotheses and to the fitting of parametric models to non-neutral data.

[1]  J. Mosimann,et al.  A New Characterization of the Dirichlet Distribution Through Neutrality , 1980 .

[2]  J. Atchison,et al.  Logistic-normal distributions:Some properties and uses , 1980 .

[3]  D. Ratcliff,et al.  No-association of proportions , 1978 .

[4]  A. M. Mathai,et al.  Exact percentage points for testing independence , 1979 .

[5]  J. Aitchison.  A new approach to null correlations of proportions , 1981 .

[6]  I. James.  Distributions Associated with Neutrality Properties for Random Proportions , 1981 .

[7]  Null correlation for proportions , 1969 .

[8]  I. James.  Multivariate Distributions Which Have Beta Conditional Distributions , 1975 .

[9]  J. Mosimann.  On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions , 1962 .

[10]  I. James,et al.  Products of Independent Beta Variables with Application to Connor and Mosimann's Generalized Dirichlet Distribution , 1972 .

[11]  J. Mosimann.  Statistical Problems of Size and Shape. I. Biological Applications and Basic Theorems , 1975 .

[12]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[13]  Ganapati P. Patil,et al.  Statistical Distributions in Scientific Work , 1981 .

[14]  J. Darroch,et al.  A Characterization of the Dirichlet Distribution , 1971 .

[15]  J. Darroch,et al.  F-Independence and Null Correlation of Continuous, Bounded-Sum, Positive Variables , 1974 .

[16]  Robert J. Connor,et al.  Concepts of Independence for Proportions with a Generalization of the Dirichlet Distribution , 1969 .

[17]  James E. Mosimann,et al.  On the compound negative multinomial distribution and correlations among inversely sampled pollen counts , 1963 .

[18]  F. Chayes.  On correlation between variables of constant sum , 1960 .

[19]  Felix Chayes,et al.  An Approximate Statistical Test for Correlations between Proportions , 1966, The Journal of Geology.

[20]  G. S. Mudholkar,et al.  Complete Independence in the Multivariate Normal Distribution. , 1981 .

[21]  F. Chayes,et al.  Numerical Correlation and Petrographic Variation , 1962, The Journal of Geology.

[22]  K. Pearson.  Mathematical contributions to the theory of evolution.—On a form of spurious correlation which may arise when indices are used in the measurement of organs , 1897, Proceedings of the Royal Society of London.