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User:BeyondNormality/Adhikari-Sarkar distribution (type 1)

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Adhikari-Sarkar distribution (type 1)
Notation
Parameters n ∈
Support x ∈ {1, 2, 3, ... , 9}
PMF
CDF
Mean
Median
Mode
Variance
Skewness
Excess kurtosis
Entropy
MGF
CF
PGF

Also known as the distribution of most significant digit, the probability mass function of the Adhikari-Sarkar distribution (type 1) is given by


Cumulative Distribution Function


Expected Value


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
Furlan's spectrum of power numbers
Uppuluri-Patil (type 1)
Uppuluri-Patil (type 2)
Uppuluri-Patil (type 3)
Benford or

References

[edit]
  • Adhikari, I.S., Sarkar, B.P. (1968). Distribution of most significant digit in certain functions whose arguments are random variables. Sankhyā B 30, 47-58
  • Uppuluri, V.R.R, Patil, S.A. (1985). The distribution of the first j digits of beta related random variables Communications in Statistics - Simulation and Computation 14, 467-472.
  • Wimmer, G., Altmann. (1999). Thesaurus of univariate discrete probability distributions. Stamm; 1. ed (1999), pg 3