Distributions
Main references: [1].
Notations
- \(Y\): a random variable
- \(\pr\rdb{Y\mid\theta}\): the probability of \(Y\)
- \(p(y\mid\theta)=\pr\rdb{Y=y\mid\theta}\): the discrete probability density function
- \(f(y\mid\theta)=\dfrac{\dl1}{\dl1y}\pr\rdb{Y\leq y\mid\theta}\): the continuous probability density function
- \(\Exp\rdb{Y}\): the expectation of \(Y\)
- \(\Var\rdb{Y}\): the variance of \(Y\)
Distributions
- \(\distbinom(n,\theta)\): Binomial distribution.
- \(\distbeta(\alpha,\beta)\): Beta distribution.
- \(\distpois(\lambda)\): Poisson distribution.
- \(\distgamma(\lambda)\): Gamma distribution.
- \(\distexp(\lambda)\): Exponential distribution.
- \(\distnormal(\mu,\sigma^2)\): Nomral distribution.
pdfs
- \(\displaystyle \pdfbinom(y, n, \theta)=\dbinom{n}{y} \theta^{y}(1-\theta)^{n-y}\).
- \(\displaystyle \pdfbeta(\theta, \alpha, \beta)=\dfrac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\theta^{\alpha-1}(1-\theta)^{\beta-1}\).
- \(\displaystyle \pdfpois\)
- \(\displaystyle \pdfgamma\)
- \(\displaystyle \pdfexp\)
- \(\displaystyle \pdfnormal\)