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In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible.
Suppose we have samples of two discrete random variables, X and Y.By constructing the joint distribution, P X,Y (x, y), from which we can calculate the conditional distributions, P X|Y (x|y) = P X,Y (x, y)/P Y (y) and P Y|X (y|x) = P X,Y (x, y)/P X (x), and calculating the various entropies, we can determine the degree of association between the two variables.
In the 2-dimensional case, if the density exists, each iso-density locus (the set of x 1,x 2 pairs all giving a particular value of ()) is an ellipse or a union of ellipses (hence the name elliptical distribution). More generally, for arbitrary n, the iso-density loci are unions of ellipsoids. All these ellipsoids or ellipses have the common ...
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.
Isoelastic utility for different values of . When > the curve approaches the horizontal axis asymptotically from below with no lower bound.. In economics, the isoelastic function for utility, also known as the isoelastic utility function, or power utility function, is used to express utility in terms of consumption or some other economic variable that a decision-maker is concerned with.
1. A measured temperature value is read every day. Decisive influencing variables are ambient temperature and air pressure, which can vary every day. 2. The measurement uncertainty strongly depends on the size of the measured value itself, e.g. amplitude-proportional.
ISO 1 is an international standard set by the International Organization for Standardization that specifies the standard reference temperature for geometrical product specification and verification. The temperature is fixed at 20 degrees Celsius (°C), which exactly equals both 293.15 kelvin (K) and 68 degrees Fahrenheit (°F).
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 ...