Resources
This space serves as a repository for reference materials, study notes, cheat sheets, and technical guides compiled throughout my studies and research.
Posts below are arranged chronologically—spanning probability theory, machine learning, software tools, and computational notes. You can also use the Archive to browse all articles organized by tags.
Selected notes have also been compiled into standalone PDF documents:
3.9. Infinitely divisible distributions
A certain kind of well behaving distributions has characteristic functions that can be represented in canonical form. In this section we cover conditions that such distributions have and its canonical representation.
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3.10. Limit theorems in ℝᵈ
This part covers limit theorems regarding random vectors $\mathbf{X} = (X_1,\cdots,X_d)’\in\mathbb{R}^d.$
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3.6. Poisson convergence
I would like to finish reviewing Probability theory I by briefly mentioning the Poisson convergence (section 3.6) and limit theorems in $\mathbb{R}^d$ (3.10).
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3.4. Central limit theorem
Now that we have all the right tools, we state and prove the central limit theorem (CLT for short), starting from the simplest form for i.i.d. cases and to Lindeberg and Lyapounov conditions.
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3.3. Characteristic functions
In undergraduate statistics, we learned moment generating functions and that it uniquely determines the distribution if exists. However moment generating function does not always exsits for all distributions. Characteristic functions always exists for all real-valued random variables and it provides alternative approach to working with distributions.
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