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User:BeyondNormality/Ahmad-Kudo-Poisson distribution

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Ahmad-Kudo-Poisson distribution
Notation
Support x ∈ { 0, 1, 2, ... }
PMF
CDF
Mean
Median
Mode
Variance
Skewness
Excess kurtosis
Entropy
MGF
CF
PGF

Also known as the modified Poisson distribution, the probability mass function of the Ahmad-Kudo-Poisson distribution is given by



Cumulative Distribution Function


Expected Value


Variance


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
deterministic
Poisson

References

[edit]
  • Ahmad, M., Kudo, A. (1967). Modified and partially truncated Poisson distribution Bulletin of the Institute of Statistical Research and Training, University of Dacca 1, 82-90
  • Wimmer, G., Altmann. (1999). Thesaurus of univariate discrete probability distributions. Stamm; 1. ed (1999), pg 5