Notation | |||
---|---|---|---|
Parameters | |||
Support | |||
PMF | |||
CDF | |||
Mean | |||
Median | |||
Mode | |||
Variance | |||
Skewness | |||
Excess kurtosis | |||
Entropy | |||
MGF | |||
CF | |||
PGF |
The probability mass function of the Barlett distribution is given by
Expected Value
Variance
Moment Generating Function
Characteristic Function
Probability Generating Function
Interrelations
editSymbol | 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 |
---|---|---|
Poisson geometric | ||
Poisson generalized Poisson family | ||
Charlier | ||
Lüders | ||
Poisson-negative binomial convolution | ||
multiple Poisson | ||
geometric | ||
Poisson |
References
edit- Bartlett, M.S. (1969). Distributions associated with cell populations. Biometrika 56, 391-400.
- Berg, S., Jaworski, J. (1988). Modified binomial and Poisson distributions with applications in random mapping theory. J. of Statistical Planning and Inference 18, 313-322.
- Samaniego, F.J. (1976). A characterization of convoluted Poisson distributions with applications to estimation. J. of the American Statistical Association 71, 475-479.
- Wimmer, G., Altmann. (1996a). The multiple Poisson distribution, its characteristics and a variety of forms. Biometrical J. 8, 995-1011
- Wimmer, G., Altmann. (1999). Thesaurus of univariate discrete probability distributions. Stamm; 1. ed (1999), pg 14