Cumulant
Cumulant Cumulants of probability distributions In probability theory ... moment-generating function is therefore called the cumulant-generating function. In case some of the ... of cumulants Invariance and equivariance The first cumulant is shift-equivariant; all of the others ... denote by κ n (X) the nth cumulant of the probability distribution of the random ... e., c is added to the first cumulant, but all higher cumulants are unchanged. ...
http://en.wikipedia.org/wiki/Cumulant - 22k - Cached - Similar pages

Talk:Cumulant
Talk:Cumulant The formula $E\backslash left(e^\{tX\; ...\; right)=0$ Zero is not a cumulant, and so the function $\backslash frac\{d\; ...\; 2t+\backslash cdots$ better deserves the name 'cumulant generation function'. Bo Jacoby 12:55, 4 ... agree that there's no zeroth-order cumulant. But I don't think that's ... t n /n! is not the nth cumulant, and that is potentially confusing. Besides, ...
http://en.wikipedia.org/wiki/Talk:Cumulant - 4k - Cached - Similar pages

Law of total cumulance
Law of total cumulance Main article: cumulant In probability theory and mathematical statistics, the ... X 1 , ..., X n ) is the joint cumulant of n random variables X 1 , ..., X ... i ∈ B | Y) is a conditional cumulant given the value of the random variable ... either 2 or 3 is the nth cumulant the same as the nth central moment ... W m are independent, then the nth cumulant is additive: $\backslash kappa\_n(W\_1+\backslash cdots+\; ...$
http://en.wikipedia.org/wiki/Law_of_total_cumulance - 11k - Cached - Similar pages

Multiset
... multisets of elements from an n-set. Cumulant generating function A natural number, n, can ... cumulants, and so g is called the cumulant-generating function. The set of nonnegative integers ... are undefined. Nevertheless the set has a cumulant-generating function, −log(1−e s ) , for s ... numbers can also be represented by a cumulant-generating function, even if it cannot be ... energy levels of a physical system. The cumulant-generating function of the multiset of ...
http://en.wikipedia.org/wiki/Multiset - 17k - Cached - Similar pages

Skewness
... defined as the ratio of the third cumulant $\backslash kappa\_3$ and the third power ... of the square root of the second cumulant $\backslash kappa\_2$: $\backslash gamma\_1\; =\; \backslash frac\{\backslash kappa\_3\; ...\; kurtosis,\; which\; is\; expressed\; as\; the\; fourth$cumulant divided by the fourth power of the square root of the second cumulant. For a sample of N values the ... unique symmetric unbiased estimator of the third cumulant and $k\_2$ is the ...
http://en.wikipedia.org/wiki/Skewness - 5k - Cached - Similar pages

Skewness (Psychology wiki)
... defined as the ratio of the third cumulant $\backslash kappa\_3$ and the third power ... of the square root of the second cumulant $\backslash kappa\_2$: $\backslash gamma\_1\; =\; \backslash frac\{\backslash kappa\_3\; ...\; kurtosis,\; which\; is\; expressed\; as\; the\; fourth$cumulant divided by the fourth power of the square root of the second cumulant. For a sample of N values the ... unique symmetric unbiased estimator of the third cumulant and $k\_2$ is the ...
http://psychology.wikia.com/wiki/Skewness - 6k - Cached - Similar pages

Moment about the mean
... when n ≥ 4 is the nth cumulant κ n (X). For n = 1, the nth cumulant is just the expected value; for n = either 2 or 3, the nth cumulant is just the nth central moment; for n ≥ 4, the nth cumulant is an nth-degree monic polynomial in ... the first n central moments. See also cumulant moment (mathematics) image moments
http://en.wikipedia.org/wiki/Moment_about_the_mean - 4k - Cached - Similar pages

Moment about the mean (Psychology wiki)
... when n ≥ 4 is the nth cumulant κ n (X). For n = 1, the nth cumulant is just the expected value; for n = either 2 or 3, the nth cumulant is just the nth central moment; for n ≥ 4, the nth cumulant is an nth-degree monic polynomial in ... first n central moments. [edit] See also cumulant moment (mathematics) image moments This page ...
http://psychology.wikia.com/wiki/Moment_about_the_mean - 6k - Cached - Similar pages

Talk:Exponential family
... in its own right, as it the cumulant-generating function of the probability distribution of ... its own right, as it is the cumulant-generating function of the probability distribution of ... t make sense without those words. A cumulant-generating function is always a cumulant-generating function of some particular probability distribution ...
http://en.wikipedia.org/wiki/Talk:Exponential_family - 9k - Cached - Similar pages

Talk:Poisson distribution
... the slightly more advanced concept of a Cumulant generating function we can rearrange the problem ... you without needing to solve anything (a Cumulant generating function is what you get when ... of a probability generating function). Actually, the cumulant-generating function is the logarithm of the ... article than anything about differential equations or cumulant-generating functions. Michael Hardy 02:31 Feb ...
http://en.wikipedia.org/wiki/Talk:Poisson_distribution - 23k - Cached - Similar pages