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This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the n factors of the power (1 + X) n one temporarily labels the term X with an index i (running from 1 to n), then each subset of k indices gives after expansion a contribution X k, and the coefficient of ...
This test procedure is based on the statistic whose sampling distribution is approximately a Chi-Square distribution with (k − 1) degrees of freedom, where k is the number of random samples, which may vary in size and are each drawn from independent normal distributions. Bartlett's test is sensitive to departures from normality.
In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or r φ) is a measure of association for two binary variables.. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975.
The formula can be understood as follows: p k q n−k is the probability of obtaining the sequence of n independent Bernoulli trials in which k trials are "successes" and the remaining n − k trials result in "failure".
Then, at each of the n measured points, the weight of the original value on the linear combination that makes up the predicted value is just 1/k. Thus, the trace of the hat matrix is n/k. Thus the smooth costs n/k effective degrees of freedom. As another example, consider the existence of nearly duplicated observations.
In mathematics, the K-function, typically denoted K(z), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to the gamma function. Definition [ edit ]
The growth constant k is the frequency (number of times per unit time) of growing by a factor e; in finance it is also called the logarithmic return, continuously compounded return, or force of interest. The e-folding time τ is the time it takes to grow by a factor e. The doubling time T is the time it takes to double.
A test statistic is the output of a scalar function of all the observations. This statistic provides a single number, such as a t-statistic or an F-statistic. As such, the test statistic follows a distribution determined by the function used to define that test statistic and the distribution of the input observational data.