- Probability Distribution Functions
- Cumulative distribution function (CDF), $F(x)$, and properties
- Probability density function (pdf), $f(x)$, and properties
- Concepts of Life-time Distributions
- Survival function: $S(x) = 1 - F(x)$, analogous to $F(x)$
- Hazard rate function $h(x) = f(x)/S(x)$, analougous to $f(x)$
- Non-parametric Estimation of Distribution
- Empirical cumulative distribution function (ECDF): $F_n(x)$
- Kernel density estimation (KDE): $\hat{f}_h(x)=\frac{1}{nh} \sum_{i=1}^n K[(x-x_i)/n]$
- Lecture Note
- Probability Distribution and Estimation[HTML]
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- Shape Analysis
- Density Shape: modeling statistical processes and quality.
- Hazard Rate Shape: modeling survival and reliability failure.
- CDF: comparing two distributions visually and statistially.
- R libraries and Functions
- R base libraries: commonly use parametric distributions
- Familiar with R function
ecdf()
- Familiar with R function
density()
- Written Assignment #1:
- Due: Tuesday, 2/3/2026 at 11:30 PM
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