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The probability density estimated in this way can then be used to calculate the entropy estimate, in a similar way to that given above for the histogram, but with some slight tweaks. One of the main drawbacks with this approach is going beyond one dimension: the idea of lining the data points up in order falls apart in more than one dimension.
In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.
The above definition is for discrete random variables. The continuous version of discrete conditional entropy is called conditional differential (or continuous) entropy. Let and be a continuous random variables with a joint probability density function (,).
If the probability density function of a random variable (or vector) X is given as f X (x), it is possible (but often not necessary; see below) to calculate the probability density function of some variable Y = g(X).
In probability theory and statistics, the index of dispersion, [1] dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard ...
The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.
The two parameters are p 1 and p 2 are specified by determining a cutscore (threshold) for examinees on the proportion correct metric, and selecting a point above and below that cutscore. For instance, suppose the cutscore is set at 70% for a test. We could select p 1 = 0.65 and p 2 = 0.75. The test then evaluates the likelihood that an ...
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.