random notes

statistics

Probability

long term relative frequency.

Random variables

function which takes outcome as input and real number as output

Probability distributions

• plot of random variable Vs. relative frequency
• Continous
  • Gamma -> beta & weibull
  • normal($ \mu , \sigma $)
  • lognormal
  • exponential($\lambda$)
  • Beta
  • t-distribution -> cauchy, heavy tailed compared to normal

Estimation

• estimator = function which gives estimate
• estimate is a random variables
• unbiased and consistent estimators is one of the primary goals
• estimation can be used for inference
• statistics like sample mean, median, trimmed mean, extreme mean etc are estimated

inference and confidence intervals

• p-value
• significance level
• sample size effect on interval length

regression

• SST = SSE + SSR
• Least squares is MLE for regression coefficient

alternative approaches to inference

• normality assumption wrong
• t-distribution based inference is worse than Wilcoxon signed rank test
• rank tests
• Bayesian inference, credibility interval Vs. confidence interval