Fisher's z-distribution
Statistical distribution
Probability density function | |||
Parameters | deg. of freedom | ||
---|---|---|---|
Support | |||
Mode |
Fisher's z-distribution is the statistical distribution of half the logarithm of an F-distribution variate:
It was first described by Ronald Fisher in a paper delivered at the International Mathematical Congress of 1924 in Toronto.[1] Nowadays one usually uses the F-distribution instead.
The probability density function and cumulative distribution function can be found by using the F-distribution at the value of . However, the mean and variance do not follow the same transformation.
The probability density function is[2][3]
where B is the beta function.
When the degrees of freedom becomes large (), the distribution approaches normality with mean[2]
and variance
Related distribution
- If then (F-distribution)
- If then
References
- ^ Fisher, R. A. (1924). "On a Distribution Yielding the Error Functions of Several Well Known Statistics" (PDF). Proceedings of the International Congress of Mathematics, Toronto. 2: 805–813. Archived from the original (PDF) on April 12, 2011.
- ^ a b Leo A. Aroian (December 1941). "A study of R. A. Fisher's z distribution and the related F distribution". The Annals of Mathematical Statistics. 12 (4): 429–448. doi:10.1214/aoms/1177731681. JSTOR 2235955.
- ^ Charles Ernest Weatherburn (1961). A first course in mathematical statistics.
External links
- MathWorld entry
- v
- t
- e
Probability distributions (list)
univariate
with finite support |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- Multinomial
- Continuous:
- Dirichlet
- Multivariate Laplace
- Multivariate normal
- Multivariate stable
- Multivariate t
- Normal-gamma
- Matrix-valued:
- LKJ
- Matrix normal
- Matrix t
- Matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- Univariate von Mises
- Wrapped normal
- Wrapped Cauchy
- Wrapped exponential
- Wrapped asymmetric Laplace
- Wrapped Lévy
- Bivariate (spherical)
- Kent
- Bivariate (toroidal)
- Bivariate von Mises
- Multivariate
- von Mises–Fisher
- Bingham
and singular
- Degenerate
- Dirac delta function
- Singular
- Cantor
- Category
- Commons