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In particle physics, CLs [1] represents a statistical method for setting upper limits (also called exclusion limits [2]) on model parameters, a particular form of interval estimation used for parameters that can take only non-negative values.
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value.
This is a list of limits for common functions such as elementary functions. In this article, the terms a, b and c are constants with respect to x.
The probability density function (PDF) for the Wilson score interval, plus PDF s at interval bounds. Tail areas are equal. Since the interval is derived by solving from the normal approximation to the binomial, the Wilson score interval ( , + ) has the property of being guaranteed to obtain the same result as the equivalent z-test or chi-squared test.
A tolerance interval (TI) is a statistical interval within which, with some confidence level, a specified sampled proportion of a population falls. "More specifically, a 100×p%/100×(1−α) tolerance interval provides limits within which at least a certain proportion (p) of the population falls with a given level of confidence (1−α)."
For example, to calculate the 95% prediction interval for a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 1, then z is approximately 2. Therefore, the lower limit of the prediction interval is approximately 5 ‒ (2⋅1) = 3, and the upper limit is approximately 5 + (2⋅1) = 7, thus giving a prediction interval of ...
For x < 1, we can calculate limits based on the fact that between 1 and 2, ...
The Bekenstein bound limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area. Thermodynamics limit the data storage of a system based on its energy, number of particles and particle modes. In practice, it is a stronger bound than the Bekenstein bound.