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User:BeyondNormality/Additive binomial distribution

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Additive binomial distribution
Notation
Parameters n ∈
0 < p < 1
a (see article)
q=1-p
Support x ∈ { 0, 1, 2, ... , n}
PMF
CDF
Mean
Median
Mode
Variance
Skewness
Excess kurtosis
Entropy
MGF
CF
PGF

Also known as the additive generalization of the binomial distribution and correlated binomial distribution, the probability mass function of the additive binomial distribution is given by



Expected Value


Variance


Recurrence Relation


Moment Generating Function


Characteristic Function


Probability Generating Function


Interrelations

[edit]
Symbol Meaning
: the random variable X is distributed as the random variable Y
the distribution in the title is identical with this distribution
the distribution in title is a special case of this distribution
this distribution is a special case of the distribution in the title
this distribution converges to the distribution in the title
the distribution in the title converges to this distribution
Relationship Distribution When
Paul-negative hypergeometric
binomial
deterministic
zero-one
Poisson

References

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  • Altham, P. (1978). Two generalizations of the binomial distribution. Applied Statistics 27, 162-167
  • Altmann-Fitter (1994). Iterative Anpassung diskreter Wahrscheinlichkeitsverteilungen. Lüdenscheid:RAM-Verlag.
  • Bahadur, R.R. (1961). A representation of the joint distribution of responses to n dichotomous items. In: Solomon. H (ed.), Studies in Item Analysis and Prediction: 158-168. Stanford: Stanford University
  • Engel, B., Brake, J. de (1993). Analysis of embryonic development with a model for under-or overdispersion relative to binomial variation. Biometrics 49, 269-279.
  • Haseman, J.K. Kupper, L.L. (1979). Analysis of dichotomous response data from certain toxicological experiments. Biometrics 35, 281-293
  • Johnson, N.L., Kotz, S., Kemp, A.W. (1992). Univariate Discrete Distributions. New York: Wiley. pg 148ff
  • Kupper, L.L., Haseman, J.K. (1978). The use of a correlated binomial model for the analysis of certain toxicological experiments. Biometrica 34, 69-76.
  • Lord, F.M. (1965). A strong true-score theory, with applications. Psychometrika 30, 239-270.
  • Paul, S.R. (1982). Analysis of proportions of affected foetuses in teratological experiments. Biometrics 38, 361-370
  • Paul, S.R. (1985). A three-parameter generalization of the binomial distribution. Communications in Statistics - Theory and Methods 14, 1497-1506
  • Paul, S.R. (1987). On the beta-correlated binomial (BCB) distribution - a three parameter generalization of the binomial distribution. Communications in Statistics - Theory and Methods 16, 1473-1478
  • Rudolpher, S.M. (1990). A Markov chain model of extrabinomial variations. Biometrika 77, 255-264
  • Tarone, R.F. (1979). Testing the goodness of fit of the binomial distribution. Biometrika 66, 585-590
  • Wilcox, R.R. (1981). A review of the beta-binomial model and its extensions. J. of Educational Statistics 6, 3-32
  • Wimmer, G., Altmann. (1999). Thesaurus of univariate discrete probability distributions. Stamm; 1. ed (1999), pg 2