Octave has functions for computing the Probability Density Function (PDF), the Cumulative Distribution function (CDF), and the quantile (the inverse of the CDF) for a large number of distributions.
The following table summarizes the supported distributions (in alphabetical order).
Distribution | CDF | Quantile
| |
---|---|---|---|
Beta Distribution | betapdf
| betacdf
| betainv
|
Binomial Distribution | binopdf
| binocdf
| binoinv
|
Cauchy Distribution | cauchy_pdf
| cauchy_cdf
| cauchy_inv
|
Chi-Square Distribution | chi2pdf
| chi2cdf
| chi2inv
|
Univariate Discrete Distribution | discrete_pdf
| discrete_cdf
| discrete_inv
|
Empirical Distribution | empirical_pdf
| empirical_cdf
| empirical_inv
|
Exponential Distribution | exppdf
| expcdf
| expinv
|
F Distribution | fpdf
| fcdf
| finv
|
Gamma Distribution | gampdf
| gamcdf
| gaminv
|
Geometric Distribution | geopdf
| geocdf
| geoinv
|
Hypergeometric Distribution | hygepdf
| hygecdf
| hygeinv
|
Kolmogorov Smirnov Distribution | Not Available | kolmogorov_smirnov_cdf
| Not Available
|
Laplace Distribution | laplace_pdf
| laplace_cdf
| laplace_inv
|
Logistic Distribution | logistic_pdf
| logistic_cdf
| logistic_inv
|
Log-Normal Distribution | lognpdf
| logncdf
| logninv
|
Univariate Normal Distribution | normpdf
| normcdf
| norminv
|
Pascal Distribution | nbinpdf
| nbincdf
| nbininv
|
Poisson Distribution | poisspdf
| poisscdf
| poissinv
|
Standard Normal Distribution | stdnormal_pdf
| stdnormal_cdf
| stdnormal_inv
|
t (Student) Distribution | tpdf
| tcdf
| tinv
|
Univariate Discrete Distribution | unidpdf
| unidcdf
| unidinv
|
Uniform Distribution | unifpdf
| unifcdf
| unifinv
|
Weibull Distribution | wblpdf
| wblcdf
| wblinv
|
For each element of x, compute the probability density function (PDF) at x of the Beta distribution with parameters a and b.
For each element of x, compute the cumulative distribution function (CDF) at x of the Beta distribution with parameters a and b.
For each element of x, compute the quantile (the inverse of the CDF) at x of the Beta distribution with parameters a and b.
For each element of x, compute the probability density function (PDF) at x of the binomial distribution with parameters n and p, where n is the number of trials and p is the probability of success.
For each element of x, compute the cumulative distribution function (CDF) at x of the binomial distribution with parameters n and p, where n is the number of trials and p is the probability of success.
For each element of x, compute the quantile (the inverse of the CDF) at x of the binomial distribution with parameters n and p, where n is the number of trials and p is the probability of success.
For each element of x, compute the probability density function (PDF) at x of the Cauchy distribution with location parameter location and scale parameter scale > 0. Default values are location = 0, scale = 1.
For each element of x, compute the cumulative distribution function (CDF) at x of the Cauchy distribution with location parameter location and scale parameter scale. Default values are location = 0, scale = 1.
For each element of x, compute the quantile (the inverse of the CDF) at x of the Cauchy distribution with location parameter location and scale parameter scale. Default values are location = 0, scale = 1.
For each element of x, compute the probability density function (PDF) at x of the chi-square distribution with n degrees of freedom.
For each element of x, compute the cumulative distribution function (CDF) at x of the chi-square distribution with n degrees of freedom.
For each element of x, compute the quantile (the inverse of the CDF) at x of the chi-square distribution with n degrees of freedom.
For each element of x, compute the probability density function (PDF) at x of a univariate discrete distribution which assumes the values in v with probabilities p.
For each element of x, compute the cumulative distribution function (CDF) at x of a univariate discrete distribution which assumes the values in v with probabilities p.
For each element of x, compute the quantile (the inverse of the CDF) at x of the univariate distribution which assumes the values in v with probabilities p.
For each element of x, compute the probability density function (PDF) at x of the empirical distribution obtained from the univariate sample data.
For each element of x, compute the cumulative distribution function (CDF) at x of the empirical distribution obtained from the univariate sample data.
For each element of x, compute the quantile (the inverse of the CDF) at x of the empirical distribution obtained from the univariate sample data.
For each element of x, compute the probability density function (PDF) at x of the exponential distribution with mean lambda.
For each element of x, compute the cumulative distribution function (CDF) at x of the exponential distribution with mean lambda.
The arguments can be of common size or scalars.
For each element of x, compute the quantile (the inverse of the CDF) at x of the exponential distribution with mean lambda.
For each element of x, compute the probability density function (PDF) at x of the F distribution with m and n degrees of freedom.
For each element of x, compute the cumulative distribution function (CDF) at x of the F distribution with m and n degrees of freedom.
For each element of x, compute the quantile (the inverse of the CDF) at x of the F distribution with m and n degrees of freedom.
For each element of x, return the probability density function (PDF) at x of the Gamma distribution with shape parameter a and scale b.
For each element of x, compute the cumulative distribution function (CDF) at x of the Gamma distribution with shape parameter a and scale b.
For each element of x, compute the quantile (the inverse of the CDF) at x of the Gamma distribution with shape parameter a and scale b.
For each element of x, compute the probability density function (PDF) at x of the geometric distribution with parameter p.
For each element of x, compute the cumulative distribution function (CDF) at x of the geometric distribution with parameter p.
For each element of x, compute the quantile (the inverse of the CDF) at x of the geometric distribution with parameter p.
Compute the probability density function (PDF) at x of the hypergeometric distribution with parameters t, m, and n. This is the probability of obtaining x marked items when randomly drawing a sample of size n without replacement from a population of total size t containing m marked items.
The parameters t, m, and n must be positive integers with m and n not greater than t.
Compute the cumulative distribution function (CDF) at x of the hypergeometric distribution with parameters t, m, and n. This is the probability of obtaining not more than x marked items when randomly drawing a sample of size n without replacement from a population of total size t containing m marked items.
The parameters t, m, and n must be positive integers with m and n not greater than t.
For each element of x, compute the quantile (the inverse of the CDF) at x of the hypergeometric distribution with parameters t, m, and n. This is the probability of obtaining x marked items when randomly drawing a sample of size n without replacement from a population of total size t containing m marked items.
The parameters t, m, and n must be positive integers with m and n not greater than t.
Return the cumulative distribution function (CDF) at x of the Kolmogorov-Smirnov distribution,
Inf Q(x) = SUM (-1)^k exp (-2 k^2 x^2) k = -Inffor x > 0.
The optional parameter tol specifies the precision up to which the series should be evaluated; the default is tol =
eps
.
For each element of x, compute the probability density function (PDF) at x of the Laplace distribution.
For each element of x, compute the cumulative distribution function (CDF) at x of the Laplace distribution.
For each element of x, compute the quantile (the inverse of the CDF) at x of the Laplace distribution.
For each element of x, compute the PDF at x of the logistic distribution.
For each element of x, compute the cumulative distribution function (CDF) at x of the logistic distribution.
For each element of x, compute the quantile (the inverse of the CDF) at x of the logistic distribution.
For each element of x, compute the probability density function (PDF) at x of the lognormal distribution with parameters mu and sigma. If a random variable follows this distribution, its logarithm is normally distributed with mean mu and standard deviation sigma.
Default values are mu = 1, sigma = 1.
For each element of x, compute the cumulative distribution function (CDF) at x of the lognormal distribution with parameters mu and sigma. If a random variable follows this distribution, its logarithm is normally distributed with mean mu and standard deviation sigma.
Default values are mu = 1, sigma = 1.
For each element of x, compute the quantile (the inverse of the CDF) at x of the lognormal distribution with parameters mu and sigma. If a random variable follows this distribution, its logarithm is normally distributed with mean
log (
mu)
and variance sigma.Default values are mu = 1, sigma = 1.
For each element of x, compute the probability density function (PDF) at x of the negative binomial distribution with parameters n and p.
When n is integer this is the Pascal distribution. When n is extended to real numbers this is the Polya distribution.
The number of failures in a Bernoulli experiment with success probability p before the n-th success follows this distribution.
For each element of x, compute the cumulative distribution function (CDF) at x of the negative binomial distribution with parameters n and p.
When n is integer this is the Pascal distribution. When n is extended to real numbers this is the Polya distribution.
The number of failures in a Bernoulli experiment with success probability p before the n-th success follows this distribution.
For each element of x, compute the quantile (the inverse of the CDF) at x of the negative binomial distribution with parameters n and p.
When n is integer this is the Pascal distribution. When n is extended to real numbers this is the Polya distribution.
The number of failures in a Bernoulli experiment with success probability p before the n-th success follows this distribution.
For each element of x, compute the probability density function (PDF) at x of the normal distribution with mean mu and standard deviation sigma.
Default values are mu = 0, sigma = 1.
For each element of x, compute the cumulative distribution function (CDF) at x of the normal distribution with mean mu and standard deviation sigma.
Default values are mu = 0, sigma = 1.
For each element of x, compute the quantile (the inverse of the CDF) at x of the normal distribution with mean mu and standard deviation sigma.
Default values are mu = 0, sigma = 1.
For each element of x, compute the probability density function (PDF) at x of the Poisson distribution with parameter lambda.
For each element of x, compute the cumulative distribution function (CDF) at x of the Poisson distribution with parameter lambda.
For each element of x, compute the quantile (the inverse of the CDF) at x of the Poisson distribution with parameter lambda.
For each element of x, compute the probability density function (PDF) at x of the standard normal distribution (mean = 0, standard deviation = 1).
For each element of x, compute the cumulative distribution function (CDF) at x of the standard normal distribution (mean = 0, standard deviation = 1).
For each element of x, compute the quantile (the inverse of the CDF) at x of the standard normal distribution (mean = 0, standard deviation = 1).
For each element of x, compute the probability density function (PDF) at x of the t (Student) distribution with n degrees of freedom.
For each element of x, compute the cumulative distribution function (CDF) at x of the t (Student) distribution with n degrees of freedom, i.e., PROB (t(n) ≤ x).
For each element of x, compute the quantile (the inverse of the CDF) at x of the t (Student) distribution with n degrees of freedom. This function is analogous to looking in a table for the t-value of a single-tailed distribution.
For each element of x, compute the probability density function (PDF) at x of a discrete uniform distribution which assumes the integer values 1–n with equal probability.
Warning: The underlying implementation uses the double class and will only be accurate for n ≤
bitmax
(2^53 - 1 on IEEE-754 compatible systems).
For each element of x, compute the cumulative distribution function (CDF) at x of a discrete uniform distribution which assumes the integer values 1–n with equal probability.
For each element of x, compute the quantile (the inverse of the CDF) at x of the discrete uniform distribution which assumes the integer values 1–n with equal probability.
For each element of x, compute the probability density function (PDF) at x of the uniform distribution on the interval [a, b].
Default values are a = 0, b = 1.
For each element of x, compute the cumulative distribution function (CDF) at x of the uniform distribution on the interval [a, b].
Default values are a = 0, b = 1.
For each element of x, compute the quantile (the inverse of the CDF) at x of the uniform distribution on the interval [a, b].
Default values are a = 0, b = 1.
Compute the probability density function (PDF) at x of the Weibull distribution with scale parameter scale and shape parameter shape which is given by
shape * scale^(-shape) * x^(shape-1) * exp (-(x/scale)^shape)for x ≥ 0.
Default values are scale = 1, shape = 1.
Compute the cumulative distribution function (CDF) at x of the Weibull distribution with scale parameter scale and shape parameter shape, which is
1 - exp (-(x/scale)^shape)for x ≥ 0.
Default values are scale = 1, shape = 1.