right is Prism's best-fit of a model that sums two Gaussian distributions (built-in to Prism, but I had to tweak the initial values to get it to fit). This fits the data perfectly. The graph may not have two modes, but the data are sampled from the sum of two Gaussian ...
In this paper, product of two Gaussian- Q functions is represented as sum of exponentials. It is further used to evaluate error probabilities of modulation techniques in fading distributions. The knowledge of moment generating function (MGF) is sufficient enough to derive closed-form solution to ...
Unfortunately there is no closed form expression for the sum of Rayleigh distributions \cite{1388722}. Let us attempt to use the properties of Gaussian random variables to find an approximation. The variance of the sum of two Gaussian random variables is: \begin{equation}...
Sum of independent Gaussians via change-of-variables formula Ask Question Asked 7 years, 6 months ago Modified 7 years, 5 months ago Viewed 2k times This question shows research effort; it is useful and clear 2 Save this question. Show activity on this post. Let X∼N(μ...
The cumulative distribution of the envelope of the sum of two sine waves and narrowband Gaussian noise, the difference of the phases of the sine waves being uniformly distributed over (0, 2 pi ), is expressed as an integral that is evaluated by numerical quadrature. Approximation for the distr...
class SumOfGaussians(tf.keras.layers.Layer): def __init__(self, num_gaussians, **kwargs): super(SumOfGaussians, self).__init__(**kwargs) self.num_gaussians = num_gaussians def build(self, input_shape): self.dim = input_shape[-1] self.means = self.add_weight( 'means', ...
4 the answer is yes, a finite linear combination of subgaussian random variables is itself a subgaussian random variable. we will prove this in two parts. firstly we will show (i) that if x ∼ s g ( ν ) x ∼ s g ( ν ) , then ∀ a ∈ r , a x ∼ s g ( | a ...
The variance of the sum of two independent random variables is the sum of the variances of each random variable. True or False? Variance The variance is a measure of dispersion. It measures the spread and variability of the distribution. It ...
One of the many ways of deriving the law of quadratic reciprocity and determining the sign of the quadratic Gaussian sum rests on properties of the product ∏ 1≤r≤(p-1)/2 2sin(2πr/p). The author here describes an analogous cubic produ... IV Reshetukha - 《Ukrainian Mathematical Jo...
Informational properties of the Nash solutions of two stochastic nonzero-sum games Within the framework of stochastic two-person nonzero-sum games, we deal with two commonly used models in engineering and economics鈥攏amely, the LQG (Linear-Quadratic-Gaussian) and the duopoly problems. We investiga...