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Watterson, G. A.

Models for the logarithmic species abundance distributions. (English) Zbl 0292.92003

Theor. Population Biology 6, 217-250 (1974).
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Cited in 30 Documents

MSC:

92D10 Genetics and epigenetics
62E15 Exact distribution theory in statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
62F10 Point estimation
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[1] Abramowitz, M.; Stegun, I. A., (Handbook of Mathematical Functions (1965), Dover: Dover New York)
[2] Anscombe, F. J., Sampling theory of the negative binomial and logarithmic series distributions, Biometrika, 37, 358-382 (1950) · Zbl 0039.14202
[3] Bartholomew, D. J., Stochastic Models for Social Processes (1967), Wiley: Wiley New York · Zbl 0578.92026
[4] Barton, D. E.; Mallows, C. L., Some aspects of the random sequence, Ann. Math. Statist, 36, 236-260 (1965) · Zbl 0128.13001
[5] Basharin, G. P., On a statistical estimate for the entropy of a sequence of independent random variables, Theor. Probability Appl, 4, 333-336 (1959)
[6] Bliss, C. I., An analysis of some insect trap records, (Patil, G. P., Classical and Contagious Discrete Distributions (1965), Statistical Publishing Co: Statistical Publishing Co Calcutta, India) · Zbl 0063.00458
[7] Boswell, M. T.; Patil, G. P., Chance mechanisms generating the logarithmic series distributions used in the analysis of number of species and individuals, (Patil, G. P.; Pielou, E. C.; Waters, W. E., Statistical Ecology, Vol. 1 (1971), Pennsylvania State University Press: Pennsylvania State University Press University Park, PA) · Zbl 0262.60060
[8] Bowman, K. O.; Hutcheson, K.; Odum, E. P.; Shenton, L. R., Comments on the distribution of indices of diversity, (Patil, G. P.; Pielcou, E. C.; Waters, W. E., Statistical Ecology, Vol. 3 (1971), Pennsylvania State University Press, University Press: Pennsylvania State University Press, University Press University Park, PA)
[9] Bowman, K. O.; Shenton, L. R., Properties of the maximum likelihood estimator for the parameter of the logarithmic series distribution, (Patil, G. P., Random Counts in Scientific Work, Vol. 1 (1970), Pennsylvania State University Press: Pennsylvania State University Press University Park, PA), 127-150 · Zbl 1220.62018
[10] Corbet, A. S., Results obtained with Malayan butterflies, J. Anim. Ecol, 12, 42-44 (1943)
[11] Ewens, W. J., erratum, Theor. Pop. Biol, 3, 376 (1972)
[12] Ewens, W. J., Testing for increased mutation rate for neutral alleles, Theor. Pop. Biol, 4, 251-258 (1973)
[13] Fisher, R. A., A theoretical distribution for the apparent abundance of different species, J. Anim. Ecol, 12, 54-57 (1943)
[14] Good, I. J., The population frequencies of species and the estimation of population parameters, Biometrika, 40, 237-264 (1953) · Zbl 0051.37103
[15] Guess, H. A.; Ewens, W. J., Theoretical and simulation results relating to the neutral allele theory, Theor. Pop. Biol, 3, 434-447 (1972) · Zbl 0247.92004
[16] Guttman, I., A note on a series solution of a problem in estimation, Biometrika, 45, 565-567 (1958) · Zbl 0085.13702
[17] Holgate, P., Species frequency distributions, Biometrika, 56, 651-661 (1969) · Zbl 0183.48702
[18] Karlin, S.; McGregor, J., The number of mutant forms maintained in a population, (Proc. 5th Berkeley Symp. Math. Statist. Prob, IV (1967)), 415-438
[19] Karlin, S.; McGregor, J., Addendum to a paper of W. Ewens, Theor. Pop. Biol, 3, 113-116 (1972) · Zbl 0245.92010
[20] Kendall, D. G., On some modes of population growth leading to R. A. Fisher’s logarithmic series distribution, Biometrika, 35, 6-15 (1948) · Zbl 0030.31601
[21] Kimura, M.; Crow, J. F., The number of alleles that can be maintained in a finite population, Genetics, 49, 725-738 (1964)
[22] Longuet-Higgins, M. S., On the Shannon-Weaver index of diversity in relation to the distribution of species in bird censuses, Theor. Pop. Biol, 2, 271-289 (1971) · Zbl 0235.92003
[23] McIntosh, R. P., An index of diversity and the relation of certain concepts to diversity, Ecology, 48, 392-404 (1967)
[24] Nelson, W. C.; David, H. A., The logarithmic distribution: a review, Virginia J. Sc, 18, 95-102 (1967)
[25] Owen, A. R.G., The summation of class frequencies, (Classical and Contagious Discrete Distributions (1965), Statistical Publishing Co: Statistical Publishing Co Calcutta, India), 395-397
[26] Patil, G. P., Some methods of estimation for the logarithmic series distribution, Biometrics, 18, 68-75 (1962) · Zbl 0114.10601
[27] Patil, G. P., Minimum variance unbiased estimation and certain problems of additive number theory, Ann. Math. Statist, 34, 1050-1056 (1963) · Zbl 0116.37203
[28] Patil, G. P.; Bildiker, S., On minimum variance unbiased estimation for the logarithmic series distribution, Sankhyā Ser. A, 28, 239-250 (1966) · Zbl 0203.21101
[29] Patil, G. P.; Joshi, S. W., (A Dictionary and Bibliography of Discrete Distributions (1968), Oliver and Boyd: Oliver and Boyd Edinburgh, Scotland) · Zbl 0193.18301
[30] Patil, G. P.; Wani, J. K., On certain structural properties of the logarithmic series distribution and the first type Stirling distribution, Sankhyā Ser. A, 27, 271-280 (1965) · Zbl 0168.40104
[31] Patil, G. P.; Wani, J. K., Maximum likelihood estimation for the complete and truncated logarithmic series distributions, (Patil, G. P., Classical and Contagious Discrete Distributions (1965), Statistical Publishing Co: Statistical Publishing Co Calcutta, India) · Zbl 0163.40501
[32] Pielou, E. C., An Introduction to Mathematical Ecology (1969), Wiley-Interscience: Wiley-Interscience New York · Zbl 0259.92001
[33] Quenouille, M. H., A relation between the logarithmic, Poisson and negative binomial series, Biometrics, 5, 162-164 (1949)
[34] Rao, C. R., Some comments on the logarithmic series distribution in the analysis of insect trap data, (Patil, G. P.; Pielou, E. C.; Waters, W. E., Statistical Ecology, Vol. 1 (1971), Pennsylvania State University Press: Pennsylvania State University Press University Park, PA) · Zbl 0246.62002
[35] Roy, J.; Mitra, S. K., Unbiased minimum variance estimation in a class of discrete distributions, Sankhyā, 18, 371-378 (1957) · Zbl 0084.14901
[36] Shannon, C. E., A mathematical theory of communication, Bell System Tech. J, 27, 379-423 (1948) · Zbl 1154.94303
[37] Simpson, E. H., Measurement of diversity, Nature, 163, 688 (1949) · Zbl 0032.03902
[38] Siromoney, G., Entropy of logarithmic series distributions, Sankhyā Ser. A, 24, 419-420 (1962) · Zbl 0108.32502
[39] Trajstman, A. C., On a conjecture of G. A. Watterson, Adv. Appl. Prob, 6 (1974) · Zbl 0288.92012
[40] Watterson, G. A., The sampling theory of selectively neutral alleles, Adv. Appl. Prob, 6 (1974) · Zbl 0289.62020
[41] Webb, D. J., The statistics of relative abundance and diversity, Report, C.S.I.R.O. Division of Fisheries and Oceanography, Cronulla, Australia (1973)
[42] Williamson, E.; Bretherton, M. H., Tables of the logarithmic series distribution, Ann. Math. Statist, 35, 284-297 (1964) · Zbl 0129.33504
[43] Yule, G. U., Statistical Study of Literary Vocabulary (1944), Cambridge University Press: Cambridge University Press London/New York
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