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The inverse Mills ratio is the ratio of the probability density function to the complementary cumulative distribution function of a distribution. Its use is often motivated by the following property of the truncated normal distribution.
The Miller theorem may be proved by using the equivalent two-port network technique to replace the two-port to its equivalent and by applying the source absorption theorem. [3] This version of the Miller theorem is based on Kirchhoff's voltage law; for that reason, it is named also Miller theorem for voltages.
However, according to Scheffé’s theorem, convergence of the probability density functions implies convergence in distribution. [4] The portmanteau lemma provides several equivalent definitions of convergence in distribution. Although these definitions are less intuitive, they are used to prove a number of statistical theorems.
Elitzur's theorem (quantum field theory, statistical field theory) Envelope theorem (calculus of variations) Equal incircles theorem (Euclidean geometry) Equidistribution theorem (ergodic theory) Equipartition theorem (ergodic theory) Erdős–Anning theorem (discrete geometry) Erdős–Dushnik–Miller theorem ; Erdős–Gallai theorem (graph ...
Miller's theorem generalizes to a version of Sullivan's conjecture in which the action on is allowed to be non-trivial. In, [ 3 ] Sullivan conjectured that η is a weak equivalence after a certain p-completion procedure due to A. Bousfield and D. Kan for the group G = Z / 2 {\displaystyle G=Z/2} .
Central limit theorem; Characterization of probability distributions; Cochran's theorem; Complete class theorem; Continuous mapping theorem; Cox's theorem; Cramér's decomposition theorem; Craps principle
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
These properties of the Miller effect are generalized in the Miller theorem. The Miller capacitance due to undesired parasitic capacitance between the output and input of active devices like transistors and vacuum tubes is a major factor limiting their gain at high frequencies.