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N ( 0, σ 2 ) denotes a zero mean normal distribution with variance σ2.
where the real and imaginary parts obey a zero mean normal distribution with half the original variance, respectively.
where the parameters α5 is the effective attenuation constant, C5|dB is a constant and their values are listed in Table 2. χ5|dB follows a zero mean normal distribution with a SD of 4.14 dB.
Whatever the method used to define the prior values, we suggest checking the resulting posterior distributions in order to make sure they are evenly sampled around the specified mean (normal distribution) and not centred on the highest or lowest categories (skewed distribution).
A random effect is one where the contribution from that variable for a particular measurement is a sample of a random variable; in this work, all the random variables were assumed to have zero-mean normal distributions with unknown variances.
Since the probability density function of the product of two independent zero-mean normal distributions is approximated by a modified Bessel function of the second kind, the closed form probability density function for the sum is extremely difficult to derive.
Therefore, in the simulation corresponding to Figure 13, the error of channel coefficient and angle of arrival are assumed to comply with the following zero-mean normal distributions (refer to Chapter 3 in [34]), respectively: Figure 13 Impact of imperfect channel information on the BER performance (two different train speeds 240 and 360 km/h are simulated).
We treated these 8 values as 'site means' and each mean was added to 15 observations that were randomly drawn from a zero-mean normal distribution with s.d.
σ ε 2 is the variance of the zero-mean normal distribution representing the residual error.
σ γ B k R 2 is the variance of the zero-mean normal distribution representing the background count rate contribution.
μ CF is the mean, and α _CF i is the random intercept representing a contribution specific to calibration source i. σ C F 2 is the variance of the zero-mean normal distribution of the random intercept.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com