Probability, random variables, and stochastic processes

By A. Papoulis, S. Pil-lai. 2002

1,637 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0941a4805b0d7cf85e3a921e5a39744a1630823b

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Citations in the corpus

A continuous measure of phasic electrodermal activity (2010, background): “The calculation of the moments for distinct istributions P(x) was defined as follows (Papoulis and Pillai, 2002): n (a) = ˙(x − a)n P(x) (6) The first moment about zero 1(0) equals the expected value or ean and is usually simply denoted ′1 or ; the second moment round the mean 2 = 2( ) is equal to…”
χ2 time-frequency discriminator for gravitational wave detection (2004, background): “In this paper, we imagine that n t is a random time-series drawn from a large ensemble of such timeseries, whose statistical properties are those of the instrument noise [38].”
Fluorophore localization algorithms for super-resolution microscopy (2014, methodology): “The parameters are varied to find the values that give the best ‘fit’ to the data, and fit is typically measured by either the maximum-likelihood criterion 31,34–36 or the least-squares (LS) criterion 15,16,18,37 .”
Hybrid solar/wind power system probabilistic modelling for long-term performance assessment (2006, methodology): “From (7), if the probability density function f ktðktÞ for the random variable kt is known, it is possible to obtain the probability density function f PpvðPpvÞ for Ppv by applying the fundamental theorem for function of a random variable (Papoulis, 1982).”
Spike detection using the continuous wavelet transform (2005, background): “A Note on SNR In communication theory, SNR at time is defined as the absolute value of the signal amplitude at time divided by the standard deviation of the noise [32].”
A Cross-Layer (Layer 2 + 3) Handoff Management Protocol for Next-Generation Wireless Systems (2006, methodology): “Therefore, the pdf of t is given by [25],”