The kurtosis ? is defined to be the normalised fourth central moment minus 3 ( Equivalently, as in the next section, it is the fourth cumulant divided by the square of the variance ).
32.
Where \ mu _ 4 is the fourth central moment of the distribution or population and \ gamma _ 2 = \ mu _ 4 / \ sigma ^ 4-3 is the excess kurtosis.
33.
Nonetheless, it has been possible through conversations and in some instances a new reading of the court's published opinions during the period to gain some fresh insight into some central moments in the all-consuming event.
34.
The New Oxford Annotated Apocrypha identifies a clear chiastic pattern in both " acts, " in which the order of events is reversed at a central moment in the narrative ( i . e ., abcc'b'a').
35.
May be found by matching the first two central moments of a bias, then the noncentrality \ lambda is zero and \ textrm { RSS } / \ sigma ^ 2 follows a central chi-squared distribution.
36.
Notice that in this context the usual skewness is not well defined, as for ? < 2 the distribution does not admit 2nd or higher moments, and the usual skewness definition is the 3rd central moment.
37.
He examines various cult-complexes in detail, confronting " sacrificial ritual with its tension between encountering death and affirming life, its external form consisting of preparations, a frightening central moment, and restitution ", and affirming in detail the initial hypothesis.
38.
If the " biased sample variance " ( the second central moment of the sample, which is a downward-biased estimate of the population variance ) is used to compute an estimate of the population's standard deviation, the result is
39.
This terminology for measures carries over to random variables in the usual way : if is a probability space and is a random variable, then the "'- th central moment "'of " X " about is defined to be
40.
For the second and higher moments, the "'central moments "'( moments about the mean, with " c " being the mean ) are usually used rather than the moments about zero, because they provide clearer information about the distribution's shape.
