binomialPmf
Binomial distribution: probability of exactly this outcome. Exact when p is exact. With an exact p, works up to n = 3000.
n(integer) --p(number) --k(integer) --
Probability Distributions
binomialCdf
Binomial distribution: cumulative probability P(X <= x). Exact when p is exact. With an exact p, works while n^2 * d is at most 230000, where d is the length of p's denominator (1 for 1/2 or 0.3, 3 for 0.123): n = 479 for p = 1/2, n = 276 for p = 0.123.
n(integer) --p(number) --k(integer) --
binomialMean
Binomial distribution: mean. Exact when p is exact.
n(integer) --p(number) --
binomialVariance
Binomial distribution: variance. Exact when p is exact.
n(integer) --p(number) --
normalPdf
Normal distribution: probability density at x.
x(number) --mu(number) --sigma(number) --
normalCdf
Normal distribution: cumulative probability P(X <= x).
x(number) --mu(number) --sigma(number) --
normalProb
Normal distribution: probability P(a <= X <= b).
a(number) --b(number) --mu(number) --sigma(number) --
normalQuantile
Normal distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --mu(number) --sigma(number) --
poissonPmf
Poisson distribution: probability of exactly this outcome.
lambda(number) --k(integer) --
poissonCdf
Poisson distribution: cumulative probability P(X <= x). Works up to k = 30000.
lambda(number) --k(integer) --
poissonMean
Poisson distribution: mean.
lambda(number) --
poissonVariance
Poisson distribution: variance.
lambda(number) --
uniformPdf
Continuous uniform distribution: probability density at x.
x(number) --lower(number) --upper(number) --
uniformCdf
Continuous uniform distribution: cumulative probability P(X <= x).
x(number) --lower(number) --upper(number) --
uniformQuantile
Continuous uniform distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --lower(number) --upper(number) --
uniformMean
Continuous uniform distribution: mean.
lower(number) --upper(number) --
uniformVariance
Continuous uniform distribution: variance.
lower(number) --upper(number) --
exponentialPdf
Exponential distribution: probability density at x.
x(number) --lambda(number) --
exponentialCdf
Exponential distribution: cumulative probability P(X <= x).
x(number) --lambda(number) --
exponentialSf
Exponential distribution: survival probability P(X > x).
x(number) --lambda(number) --
exponentialQuantile
Exponential distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --lambda(number) --
exponentialMean
Exponential distribution: mean.
lambda(number) --
exponentialVariance
Exponential distribution: variance.
lambda(number) --
gammaPdf
Gamma distribution: probability density at x.
x(number) --shape(number) --scale(number) --
gammaCdf
Gamma distribution: cumulative probability P(X <= x).
x(number) --shape(number) --scale(number) --
gammaQuantile
Gamma distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --shape(number) --scale(number) --
gammaMean
Gamma distribution: mean.
shape(number) --scale(number) --
gammaVariance
Gamma distribution: variance.
shape(number) --scale(number) --
betaPdf
Beta distribution: probability density at x.
x(number) --alpha(number) --beta_shape(number) --
betaCdf
Beta distribution: cumulative probability P(X <= x).
x(number) --alpha(number) --beta_shape(number) --
betaQuantile
Beta distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --alpha(number) --beta_shape(number) --
betaMean
Beta distribution: mean.
alpha(number) --beta_shape(number) --
betaVariance
Beta distribution: variance.
alpha(number) --beta_shape(number) --
chiSquarePdf
Chi-square distribution: probability density at x.
x(number) --degrees_of_freedom(number) --
chiSquareCdf
Chi-square distribution: cumulative probability P(X <= x).
x(number) --degrees_of_freedom(number) --
chiSquareQuantile
Chi-square distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --degrees_of_freedom(number) --
chiSquareSf
Chi-square distribution: survival probability P(X > x), the upper tail worked directly (accurate far into the tail).
x(number) --df(number) -- degrees of freedom
chiSquareMean
Chi-square distribution: mean.
degrees_of_freedom(number) --
chiSquareVariance
Chi-square distribution: variance.
degrees_of_freedom(number) --
lognormalPdf
Lognormal distribution: probability density at x.
x(number) --mu(number) --sigma(number) --
lognormalCdf
Lognormal distribution: cumulative probability P(X <= x).
x(number) --mu(number) --sigma(number) --
lognormalQuantile
Lognormal distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --mu(number) --sigma(number) --
lognormalSf
Lognormal distribution: survival probability P(X > x), through the normal upper tail.
x(number) --mu(number) --sigma(number) --
lognormalMean
Lognormal distribution: mean.
mu(number) --sigma(number) --
lognormalVariance
Lognormal distribution: variance.
mu(number) --sigma(number) --
studentTPdf
Student's t distribution: probability density at x.
x(number) --degrees_of_freedom(number) --
studentTCdf
Student's t distribution: cumulative probability P(X <= x).
x(number) --degrees_of_freedom(number) --
studentTQuantile
Student's t distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --degrees_of_freedom(number) --
studentTSf
Student-t distribution: survival probability P(T > t), the upper tail worked directly (accurate far into the tail).
t(number) --df(number) -- degrees of freedom
studentTMean
Student's t distribution: mean.
degrees_of_freedom(number) --
studentTVariance
Student's t distribution: variance.
degrees_of_freedom(number) --
fPdf
F distribution: probability density at x.
x(number) --numerator_df(number) --denominator_df(number) --
fCdf
F distribution: cumulative probability P(X <= x).
x(number) --numerator_df(number) --denominator_df(number) --
fQuantile
F distribution: the value x with P(X <= x) = p (inverse CDF).
p(number) --numerator_df(number) --denominator_df(number) --
fSf
F distribution: survival probability P(X > x), the upper tail worked directly.
x(number) --d1(number) -- numerator degrees of freedomd2(number) -- denominator degrees of freedom
fMean
F distribution: mean.
numerator_df(number) --denominator_df(number) --
fVariance
F distribution: variance.
numerator_df(number) --denominator_df(number) --
bernoulliPmf
Bernoulli distribution: probability of exactly this outcome.
p(number) --outcome(integer) --
bernoulliCdf
Bernoulli distribution: cumulative probability P(X <= x).
p(number) --outcome(integer) --
bernoulliMean
Bernoulli distribution: mean.
p(number) --
bernoulliVariance
Bernoulli distribution: variance.
p(number) --
geometricPmf
Geometric distribution: probability of exactly this outcome.
p(number) --trial(integer) --
geometricCdf
Geometric distribution: cumulative probability P(X <= x).
p(number) --trial(integer) --
geometricMean
Geometric distribution: mean.
p(number) --
geometricVariance
Geometric distribution: variance.
p(number) --
negativeBinomialPmf
Negative binomial distribution: probability of exactly this outcome.
successes(integer) --p(number) --failures(integer) --
negativeBinomialCdf
Negative binomial distribution: cumulative probability P(X <= x).
successes(integer) --p(number) --failures(integer) --
negativeBinomialMean
Negative binomial distribution: mean.
successes(integer) --p(number) --
negativeBinomialVariance
Negative binomial distribution: variance.
successes(integer) --p(number) --
hypergeometricPmf
Hypergeometric distribution: probability of exactly this outcome.
population(integer) --population_successes(integer) --draws(integer) --observed(integer) --
hypergeometricCdf
Hypergeometric distribution: cumulative probability P(X <= x).
population(integer) --population_successes(integer) --draws(integer) --observed(integer) --
hypergeometricMean
Hypergeometric distribution: mean.
population(integer) --population_successes(integer) --draws(integer) --
hypergeometricVariance
Hypergeometric distribution: variance.
population(integer) --population_successes(integer) --draws(integer) --
normalSf
Normal distribution: survival probability P(X > x), accurate far into the tail.
x(number) --mu(number) --sigma(number) --
normalLogSf
Normal distribution: ln P(X > x), the logarithm of the upper tail, finite where the probability itself is too small for a decimal: normalLogSf(40, 0, 1) is -804.608.
x(number) --mu(number) --sigma(number) --
normalLogCdf
Normal distribution: ln P(X <= x), the logarithm of the lower tail, finite far below the mean.
x(number) --mu(number) --sigma(number) --
gammaSf
Gamma distribution: survival probability P(X > x), accurate far into the tail.
x(number) --shape(number) --scale(number) --
betaSf
Beta distribution: survival probability P(X > x), accurate far into the tail.
x(number) --alpha(number) --beta_shape(number) --