Implementation of the Inverse Transform Sampling The probability density function of a power law distribution is given by, $$f(x\ | \ x_m,\alpha) = \frac{\alpha-1}{x_m} \left(\frac{x}{x_m}\right)^{-\alpha} \ , x>x_m$$ We can find the cumulative density function by, $$ \begin{aligned} F(x) &= \int_{-\infty}^x f(x\ | \ x_m,\alpha) \ dx\\ \\ &= \int_{-\infty}^x \frac{\alpha-1}{x_m} \left(\frac{x}{x_m}\right)^{-\alpha} I(x>x_m) \ dxContinue reading “Generation of Power Law Samples with Inverse Transform Sampling (Python, R and Julia)”
Author Archives: anilbs
Interictal Spike detection from EEG with stationary waveform classification using Support Vector Machine (SVM)
This was an original Research aimed at devising a deep learning algorithm to learn and diagnose epileptogenic patterns from an EEG which indicate that a person has had an epileptic seizure. The research employed analyzing the nonlinear energy operator (NEO) of the stationary waves and then thresholding with a semi constant calculated from the energyContinue reading “Interictal Spike detection from EEG with stationary waveform classification using Support Vector Machine (SVM)”