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A calibration curve plot showing limit of detection (LOD), limit of quantification (LOQ), dynamic range, and limit of linearity (LOL).. In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. [1]
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.
The Gaussian functions are thus those functions whose logarithm is a concave quadratic function. The parameter c is related to the full width at half maximum (FWHM) of the peak according to FWHM = 2 2 ln 2 c ≈ 2.35482 c . {\displaystyle {\text{FWHM}}=2{\sqrt {2\ln 2}}\,c\approx 2.35482\,c.}
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
If () is a general scalar-valued function of a normal vector, its probability density function, cumulative distribution function, and inverse cumulative distribution function can be computed with the numerical method of ray-tracing (Matlab code).
The way it is done there is that we have two approximately Normal distributions (e.g., p1 and p2, for RR), and we wish to calculate their ratio. [b] However, the ratio of the expectations (means) of the two samples might also be of interest, while requiring more work to develop. The ratio of their means is:
Two closely related functions are the ... which is the tail probability of the standard normal distribution. The Q-function can be expressed in terms ...
The two generalized normal families described here, like the skew normal family, are parametric families that extends the normal distribution by adding a shape parameter. Due to the central role of the normal distribution in probability and statistics, many distributions can be characterized in terms of their relationship to the normal ...