Hodgetts, T E
(1995)
*The random uncertainty distribution of measurements of a complex quantity with partial-correlated real and imaginary parts (or any pair of partially-correlated variables).*
NPL Report.
DES 142

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## Abstract

This report presents a rigorous derivation, from first principles, of the random uncertainty distribution of a sample of measurements of a complex number, allowing for partial linear correlation between the complex number's real and imaginary parts, and assuming that the underlying law of joint distribution of the real and imaginary parts is the law of Gaussian normal correlation. This is the equivalent in two dimensions of the "Student's t" distribution in one dimension. The principal result is an expression for the probability that the underlying true value of the complex number is in the neighbourhood of any particular point in the complex plane, in terms of the means of the sample's real and imaginary parts, their standard deviations and their correlation coefficient. This probability density distribution is such that the contours of equal probability density are ellipses centred on the sample's two-dimensional mean, and a simple closed-form expression is given for the probability that the true value is inside any particular ellipse, which relates directly to the customary expression by confidence levels of uncertainties in measurement.

Item Type: | Report/Guide (NPL Report) |
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NPL Report No.: | DES 142 |

Subjects: | Electromagnetics |

Last Modified: | 02 Feb 2018 13:19 |

URI: | http://eprintspublications.npl.co.uk/id/eprint/323 |

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