User:BeyondNormality/Abakuks distribution

Abakuks
Notation
Parameters a>0, r ∈ { 2, 3, ... , n} , n ∈ { 2, 3, 4, ... }
Support x ∈ { r-1, r, r+1, ... , n}
PMF
CDF
Mean
Median
Mode
Variance
Skewness
Excess kurtosis
Entropy
MGF
CF
PGF


The probability mass function of the Abakuks distribution is

Recurrence relation

Expected Value

Moment Generating Function

Characteristic Function

Probability Generating Function


Interrelations

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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
  generalized power series family    
    displaced Kapur-hypergeometric family    
  Kemp-Dacey-hypergeometric family (II/20)  

References

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  • Ababuks, A. (1976). An invariance property of the Poisson distributions for a limited immigrant population. J. of the Royal Statistical Society B 38, 99-101
  • Wimmer, G., Altmann. (1999). Thesaurus of univariate discrete probability distributions. Stamm; 1. ed (1999), pg 1