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The required probability density function (PDF) is gained by smoothing over points in the two dimensional PCA-plane (Parzen window approach [46], [ 47, Chapter 4.3]).
Since anomalous diffusion is assumed to be governed by a time-fractional diffusion equation, its fundamental solution is the required probability density function.
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Requiring probability density distribution functions of uncertain variables, it is difficult for conventional structural reliability analysis methods to calculate the reliability of composite laminates with both random and interval variables.
This heuristic approach is common in optimisation techniques, but is essential in determining required probability and cumulative density distributions.
To see this observe that the required probability is given by Here, f k and F k, respectively, denote the probability density function and the cumulative distribution function of Exp(a k).
Subsequently, the optimal maintenance interval is determined by the required probability and failure probability distribution.
In downlink throughput maximization with imperfect CSI, we require the probability density function of the actual power gain conditioned on the quantized power gain.
It is shown that only one unknown probabilistic function is required, namely the probability density function of the specific surface energy.
However, the calculation of the Cramér-Rao bound requires a known probability density function that describes the occurring stochastic process.
However, the density evolution is complex as it requires to obtain probability density function (PDF) of extrinsic LLRs for each iteration; in addition, it does not provide much insight about the operations of iterative decoding.
Clearly, joining these results with those obtained in Figure 8, it can be concluded that having offers the best trade off between granularity (i.e., spectral efficiency), required signalling, and the required QoS. Figure 9 Probability density function of the system throughput for nrtPS, users and different values of the factor (when the TSPS prioritization function is applied).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com