http://uk.mathworks.com/matlabcentral/answers/230010-performing-a-convolution-of-two-exponential-functions-in-matlab?s_tid=srchtitle with accepted answer by Ghada Saleh, following the key lines of that answer: symsxb c t; f1 = a*exp((-x)/(b))+1; ...
When the convolution of two natural exponential families is still a natural exponential family, then these families are either Gaussian or Poisson. We generalize this result of Letac in the case of n (n > 2) families.doi:10.1016/S0764-4442(99)80299-7Denys Pommeret...
Create confidence intervals for the autocorrelation sequence of a white noise process. Autocorrelation Function of Exponential Sequence Compute the autocorrelation of an exponential sequence and compare it to the analytic result. Cross-Correlation of Two Exponential Sequences Compute the cross-correlatio...
Exponential Stability and Uniform Boundedness of Solutions for Nonautonomous Periodic Cauchy Problems. An Evolution Semigroup Approach. Let u μ, x, s (., 0) be the solution of the following well-posed inhomogeneous Cauchy Problem on a complex Banach space X $$left {begin{array}{ll}do... ...
Since ds/s2 = d loge s/s and the discrete wavelet transform is computed along an exponential scale sequence {aj}j with a logarithmic increment d loge s = loge a, we obtain (4.66)f[n]≈logeaCψΣj=IJ1ajWf[.,aj]⊛ψj[n]+1CψajLf[.,aj]⊛ϕJ[n]. The “.” ...
In this paper, we study the convolutions of heterogeneous exponential and geometric random variables in terms of the weakly majorization order ( ⪰ w) of parameter vectors and the likelihood ratio order ( ≥ l r). It is proved that ⪰ w order between two parameter vectors implies ≥ l ...
By expanding the exponential into its power series and using the same argument as to prove (32), we can write \begin{aligned} y(x,t)&=\sum _{\ell =0}^{\infty } \frac{(-x)^{\ell }}{\ell !} \int _{0}^{t} (t-s)^{\beta } s^{\ell }\, ds {{\textbf{v}}}\\&=...
Convolution of probability density functions If and are continuous, independent, and have probability density functions and respectively, the convolution formulae become ExampleLet be a continuous variable with support and pdf that is, has anexponential distribution. Let ...
By application of the Fourier convolution theorem, it was observed that the values of the Fourier transform of K(x) could be closely fitted by an exponential function exp(-2pilambdanu(x)) of the spatial frequency nu(x). Thereby, the line-spread function K(x) was identified as the ...
Improving representations of genomic sequence motifs in convolutional networks with exponential activations Article 08 February 2021 GINv2.0: a comprehensive topological network integrating molecular interactions from multiple knowledge bases Article Open access 13 January 2024 Data availability All data, ...