Stat

Some statistics memo written in math, Haskell, and Maxima.

References:

Mathematical Statistics with Applications (7th Edition) (Wackerly, Mendenhall, Scheaffer)
statistics-0.15.2.0

Chapter Memo

Ch.1 What is Statistics

The following function:

f k = V.length . V.filter (\x -> (av-k*sd)<x && x< (av+k*sd)) $ samples

counts the number of element within k-sigma (k=1,2,3 ..), where samples is a vector of numerical data.

Ch.2 Probability

axioms

non-negative definite
normalized
sum. rule (for mutually disjoint events)

conditional probability

P(A|B) := P(A ∩ B)/P(B), if P(B)>0, where the right hand side is read "probability of A given B."

independent events

Two events A and B are independent iff:

P(A|B) = P(A)
P(B|A) = P(B)
P(A ∩ B) = P(A)P(B)

Bayes' Rule

Ch.3 Discrete Random Variables and Their Probability Distributions

For a discrete distribution, use

probability :: d -> Int -> Double

Statistics.Distribution.Hypergeometric

hypergeometric 
  :: Int                        -- m = r in the text, the number of red 
  -> Int                        -- l = N of the total population
  -> Int                        -- k = n of the sample size
  -> HypergeometricDistribution

cumulative 
  h -- :: HypergeometricDistribution
  x -- :: y = x of a random variable

A powerful simplification can be provided by loading:

load(simplify_sum)$

Discrete Distribution	Examples and Theorems
Binomial	ex3_21.hs
Geometric	ex3_11.hs theo3_8.mac
Hypergeometric	ex3_16.hs ex3_10.mac (ex3_10.pdf) ex3_17.hs
Poisson	theo3_11.mac ex3_18.mac ex3_20.hs ex3_21.hs ex3_23.mac ex3_24.mac
Negative binomial	theo3_9.mac (no .hs code)

Ch.4 Continuous Variables and Their Probability Distributions

Continuous Distribution	TBA
Uniform
Normal
Gamma
Beta

raydsameshima/Stat