For a discrete random variable, the expected value is found by adding up the product of each possible outcome with its probability. The normal distribution is the continuous distribution, which is by far the mos
less than 0.9% of attempts require more than 3*sigma iterations, 54% of attempts require less than the mean. A typical probability distribution of percent of attempts/sigma is as follows (discretized, not centered around 0 because it deviates from the standard distribution, the mean corresponds ...
analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain. fract. calc. appl. anal. 18 , 697-716 (2015) article mathscinet math google scholar zhou, y, peng, l: on the time-fractional navier-stokes equations. comput...
type rule for the Ψ-H derivative was considered in [11]. Recently, K.A. Aldwoah et al. [1] considered the existence and Ulam-Hyers stability of solutions for a terminal valuew-Hilfer fractional differential system in different weighted spaces. However, the H- and Ψ-H fractional derivativ...
DistributionNMeanSDMedianMinMaxSkewSkurtosisFifthSixth 1100000.42.199891.05078-5.694335.341-0.2996-1.158471.847236.1398 c0c1c2c3c4c5 010000 010000 Step 4: Select a critical value Letα = 0.05. Since there are no quantile functions for mixture distributions, determine where the cumulative probability eq...
matter-constrained head model using cubic kernel convolution (no new maxima were artificially created). Then, in AFNI, sources were converted to binary values (0 and 1) using the3dcalccommand to indicate presence of solution points above the 95th percentile of values or lack thereof at each ...
Analyzing disease transmission dynamics is crucial for epidemic prevention and control. This paper introduces a Caputo fractional-order SEIHR model incorporating a generalized incidence rate. This model refines the progression of the disease through expo
In the sequel, we will use the probability density function ϑz(θ) defined on ]0,∞[ as ϑz(θ)=1zθ(1+1/z)ϖz(θ−1/z)≥0,z∈(0,1),ϖz(θ)=1π∑n=1∞(−1)n−1(θ)−zn−1Γ(nz+1)n!sin(nπz). (3) Lemma 3.1 If Eq. (2) holds, then ...
We consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenerated Fokker-Planck Diffusion; (iii) the Replicator Equation, a paradigm in Evolutionary Game Theory. While these ap...
Considering the Laplace transform for the one-sided probability density function Eq. (3.2), ∫0∞e−μsϖz(s)ds=e−μz,z∈(0,1), (3.8) and combining Eqs. (3.7) and (3.8), we obtain μz−1∫0∞E−1e−μzsC(s)E(x0+g(x))ds=∫0∞μz−1E−1e−(μη)...