Probability results of Morin's Probability for the Enthusiastic Beginner
Source:R/MorinProbabilityShelf.R
AtLeastOneOfIid.RdR arm of the Python modules of the Morin shelf (morie.fn.at_least_one_of_iid,
bayes_general, sd_of_mean, ...): counting (factorial, stars
and bars, card-hand suit patterns), the rules of probability (chain rule,
or rules, inclusion-exclusion, Bayes), independence of joint pmfs and
densities, moments of pmfs and their scaling and sums, standard
deviations of means, the exponential waiting-time density and the
correlation results of chapter 6 (regression slope, prediction
improvement, regression to the mean). Each returns the Python result's
payload as a list.
Usage
AtLeastOneOfIid(p, k = 3)
AtMostTwoSuitsProbability(n_suits = 4, n_ranks = 13, hand = 5)
BayesGeneral(priors, likelihoods)
BayesSimple(p_z_given_a, p_a, p_z)
ChainRule(p_a, p_b_given_a, p_b, p_a_given_b)
EXSquared(sigma, mu)
ExactHalfHeads(n)
ExcessScoreFactor(r)
ExpectationLinear(a, e_x, b, e_y, c)
ExponentialCrossingTime(rate_fast = 0.2, rate_slow = 0.05, ratio = 4)
ExponentialWaitingDensity(t, lam)
MorinFactorial(n)
InclusionExclusion3(p_a, p_b, p_c, p_ab, p_ac, p_bc, p_abc)
JointDensityFactorizes(grid_x, density_x, grid_y, density_y)
JointIndependent(joint, tol = 1e-09)
PmfSd(values, probs)
PmfSumConvolution(values_x, probs_x, values_y, probs_y)
PredictionImprovement(r)
ProbOrExclusive(ps)
ProbOrGeneral(p_a, p_b, p_ab)
RegressionToMeanFactor(r, y1)
SdBernoulli(p)
SdFairCoinAvg(n)
SdOfMean(sigma, n)
SdOfMeanHetero(sigmas)
SdScale(a, sigma)
SlopeFromCov(x, y)
StarsAndBars(n, N)
SuitFullHouseProbability(n_suits = 4, n_ranks = 13, k_major = 3, k_minor = 2)
VarScale(a, var_x)
VarSumWithCov(var_x, var_y, cov_xy = 0)Arguments
- p, k
Event probability and number of independent trials.
- n_suits, n_ranks, hand, k_major, k_minor
Deck and hand sizes.
- priors, likelihoods
Prior and likelihood vectors.
- p_z_given_a, p_a, p_z
Terms of the simple Bayes formula.
- p_b_given_a, p_b, p_a_given_b
Terms of the chain rule.
- sigma, mu
Standard deviation and mean.
- n
Integer size.
- r
Correlation coefficient.
- a, e_x, b, e_y, c
Coefficients and expectations.
- rate_fast, rate_slow, ratio
Exponential rates and ratio.
- t, lam
Time and rate.
- p_c, p_ab, p_ac, p_bc, p_abc
Event and intersection probabilities.
- grid_x, density_x, grid_y, density_y
Density grids.
- joint
Joint pmf table.
- tol
Tolerance.
- values, probs
Pmf support and probabilities.
- values_x, probs_x, values_y, probs_y
Two pmfs.
- ps
Probabilities of exclusive events.
- y1
First-test score deviation.
- sigmas
Standard deviations.
- x, y
Data vectors.
- N
Number of categories.
- var_x, var_y, cov_xy
Variances and covariance.