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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 first requirement ensures that the method of kernel density estimation results in a probability density function. The second requirement ensures that the average of the corresponding distribution is equal to that of the sample used. If K is a kernel, then so is the function K* defined by K*(u) = λK(λu), where λ > 0. This can be used to ...
For approximately homogeneous data, the L function has expected value t and its variance is approximately constant in t. A common plot is a graph of t − L ^ ( t ) {\displaystyle t-{\widehat {L}}(t)} against t , which will approximately follow the horizontal zero-axis with constant dispersion if the data follow a homogeneous Poisson process.
Probability density functions of the order statistics for a sample of size n = 5 from an exponential distribution with unit scale parameter In statistics , the k th order statistic of a statistical sample is equal to its k th-smallest value. [ 1 ]
K-distribution arises as the consequence of a statistical or probabilistic model used in synthetic-aperture radar (SAR) imagery. The K-distribution is formed by compounding two separate probability distributions, one representing the radar cross-section, and the other representing speckle that is a characteristic of coherent imaging. It is also ...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [ 1 ] [ 2 ] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events ( subsets of the sample space).
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
More specifically, if the likelihood function is twice continuously differentiable on the k-dimensional parameter space assumed to be an open connected subset of , there exists a unique maximum ^ if the matrix of second partials [], =,, is negative definite for every at which the gradient [] = vanishes, and if the likelihood function approaches ...