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As per available reports about 10 relevant journals, 20 Conferences, 16 workshops are presently dedicated exclusively to Probability density function and about 80 articles are being published on Probability density function.
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value. The probability of the random variable falling within a particular range of values is given by the integral of this variable’s density over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.
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Scope and Importance:
All contributing uncertainties should be expressed at the same confidence level, by converting them into standard uncertainties. A standard uncertainty is usually shown by the symbol u (small u), or u(y) (the standard uncertainty in y). The standard uncertainty is a parameter characterizing the range of values within which the true value of the measurand can be said to lie with a specified level of confidence. The standard uncertainty characterizes the uncertainty of an mean (not the spread of readings). One standard uncertainty equates to a mathematical function called the second moment, which describes the width of the probability density function (It can be thought of as "plus or minus one standard deviation"). For example when the standard uncertainty for a uniform pdf is calculated, this indicates that there is a 68% probability that the true value of the measurand will fall within the calculated range.
The coverage probability (or confidence level) in a result is increased by multiplying the standard uncertainty (u) by a constant, called the coverage factor (k) which results in the expanded uncertainty (U). In other words U = ku. For the extended uncertainty range of 2u the probability of the true value falling within the uncertainty range increases to 95%. At 3u, there is a 99% probability that the true value of the measurand will fall within this extended uncertainty range. It should be noted that Type A evaluations other coverage factors may be more appropriate. For example, a coverage factor larger than two may be used with the evaluation is based a small number of repeated measurements. The references should be consulted to learn about methods to determine other coverage factors.
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This page was last updated on April 19, 2024