Next: Tests, Previous: Correlation and Regression Analysis, Up: Statistics [Contents][Index]

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` |

- :
**betapdf***(*`x`,`a`,`b`) For each element of

`x`, compute the probability density function (PDF) at`x`of the Beta distribution with parameters`a`and`b`.

- :
**betacdf***(*`x`,`a`,`b`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the Beta distribution with parameters`a`and`b`.

- :
**betainv***(*`x`,`a`,`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`.

- :
**binopdf***(*`x`,`n`,`p`) 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.

- :
**binocdf***(*`x`,`n`,`p`) 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.

- :
**binoinv***(*`x`,`n`,`p`) 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.

- :
**cauchy_pdf***(*`x`) - :
**cauchy_pdf***(*`x`,`location`,`scale`) 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.

- :
**cauchy_cdf***(*`x`) - :
**cauchy_cdf***(*`x`,`location`,`scale`) 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.

- :
**cauchy_inv***(*`x`) - :
**cauchy_inv***(*`x`,`location`,`scale`) 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.

- :
**chi2pdf***(*`x`,`n`) For each element of

`x`, compute the probability density function (PDF) at`x`of the chi-square distribution with`n`degrees of freedom.

- :
**chi2cdf***(*`x`,`n`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the chi-square distribution with`n`degrees of freedom.

- :
**chi2inv***(*`x`,`n`) 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.

- :
**discrete_pdf***(*`x`,`v`,`p`) 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`.

- :
**discrete_cdf***(*`x`,`v`,`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`.

- :
**discrete_inv***(*`x`,`v`,`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`.

- :
**empirical_pdf***(*`x`,`data`) For each element of

`x`, compute the probability density function (PDF) at`x`of the empirical distribution obtained from the univariate sample`data`.

- :
**empirical_cdf***(*`x`,`data`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the empirical distribution obtained from the univariate sample`data`.

- :
**empirical_inv***(*`x`,`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`.

- :
**exppdf***(*`x`,`lambda`) For each element of

`x`, compute the probability density function (PDF) at`x`of the exponential distribution with mean`lambda`.

- :
**expcdf***(*`x`,`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.

- :
**expinv***(*`x`,`lambda`) For each element of

`x`, compute the quantile (the inverse of the CDF) at`x`of the exponential distribution with mean`lambda`.

- :
**fpdf***(*`x`,`m`,`n`) For each element of

`x`, compute the probability density function (PDF) at`x`of the F distribution with`m`and`n`degrees of freedom.

- :
**fcdf***(*`x`,`m`,`n`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the F distribution with`m`and`n`degrees of freedom.

- :
**finv***(*`x`,`m`,`n`) 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.

- :
**gampdf***(*`x`,`a`,`b`) For each element of

`x`, return the probability density function (PDF) at`x`of the Gamma distribution with shape parameter`a`and scale`b`.

- :
**gamcdf***(*`x`,`a`,`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`.

- :
**gaminv***(*`x`,`a`,`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`.

- :
**geopdf***(*`x`,`p`) For each element of

`x`, compute the probability density function (PDF) at`x`of the geometric distribution with parameter`p`.The geometric distribution models the number of failures (

`x`-1) of a Bernoulli trial with probability`p`before the first success (`x`).

- :
**geocdf***(*`x`,`p`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the geometric distribution with parameter`p`.The geometric distribution models the number of failures (

`x`-1) of a Bernoulli trial with probability`p`before the first success (`x`).

- :
**geoinv***(*`x`,`p`) For each element of

`x`, compute the quantile (the inverse of the CDF) at`x`of the geometric distribution with parameter`p`.The geometric distribution models the number of failures (

`x`-1) of a Bernoulli trial with probability`p`before the first success (`x`).

- :
**hygepdf***(*`x`,`t`,`m`,`n`) 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`.

- :
**hygecdf***(*`x`,`t`,`m`,`n`) 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`.

- :
**hygeinv***(*`x`,`t`,`m`,`n`) 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`.

- :
**kolmogorov_smirnov_cdf***(*`x`,`tol`) Return the cumulative distribution function (CDF) at

`x`of the Kolmogorov-Smirnov distribution.This is defined as

Inf Q(x) = SUM (-1)^k exp (-2 k^2 x^2) k = -Inf

for

`x`> 0.The optional parameter

`tol`specifies the precision up to which the series should be evaluated; the default is`tol`=`eps`

.

- :
**laplace_pdf***(*`x`) For each element of

`x`, compute the probability density function (PDF) at`x`of the Laplace distribution.

- :
**laplace_cdf***(*`x`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the Laplace distribution.

- :
**laplace_inv***(*`x`) For each element of

`x`, compute the quantile (the inverse of the CDF) at`x`of the Laplace distribution.

- :
**logistic_pdf***(*`x`) For each element of

`x`, compute the PDF at`x`of the logistic distribution.

- :
**logistic_cdf***(*`x`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the logistic distribution.

- :
**logistic_inv***(*`x`) For each element of

`x`, compute the quantile (the inverse of the CDF) at`x`of the logistic distribution.

- :
**lognpdf***(*`x`) - :
**lognpdf***(*`x`,`mu`,`sigma`) 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`= 0,`sigma`= 1.

- :
**logncdf***(*`x`) - :
**logncdf***(*`x`,`mu`,`sigma`) 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`= 0,`sigma`= 1.

- :
**logninv***(*`x`) - :
**logninv***(*`x`,`mu`,`sigma`) 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

`mu`and standard deviation`sigma`.Default values are

`mu`= 0,`sigma`= 1.

- :
**nbinpdf***(*`x`,`n`,`p`) 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.

- :
**nbincdf***(*`x`,`n`,`p`) 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.

- :
**nbininv***(*`x`,`n`,`p`) 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.

- :
**normpdf***(*`x`) - :
**normpdf***(*`x`,`mu`,`sigma`) 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.

- :
**normcdf***(*`x`) - :
**normcdf***(*`x`,`mu`,`sigma`) 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.

- :
**norminv***(*`x`) - :
**norminv***(*`x`,`mu`,`sigma`) 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.

- :
**poisspdf***(*`x`,`lambda`) For each element of

`x`, compute the probability density function (PDF) at`x`of the Poisson distribution with parameter`lambda`.

- :
**poisscdf***(*`x`,`lambda`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the Poisson distribution with parameter`lambda`.

- :
**poissinv***(*`x`,`lambda`) For each element of

`x`, compute the quantile (the inverse of the CDF) at`x`of the Poisson distribution with parameter`lambda`.

- :
**stdnormal_pdf***(*`x`) For each element of

`x`, compute the probability density function (PDF) at`x`of the standard normal distribution (mean = 0, standard deviation = 1).

- :
**stdnormal_cdf***(*`x`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the standard normal distribution (mean = 0, standard deviation = 1).

- :
**stdnormal_inv***(*`x`) 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).

- :
**tpdf***(*`x`,`n`) For each element of

`x`, compute the probability density function (PDF) at`x`of the`t`(Student) distribution with`n`degrees of freedom.

- :
**tcdf***(*`x`,`n`) For each element of

`x`, compute the cumulative distribution function (CDF) at`x`of the t (Student) distribution with`n`degrees of freedom.

- :
**tinv***(*`x`,`n`) 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.

- :
**unidpdf***(*`x`,`n`) 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`<`flintmax`

(*2^{53}*on IEEE 754 compatible systems).

- :
**unidcdf***(*`x`,`n`) 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.

- :
**unidinv***(*`x`,`n`) 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.

- :
**unifpdf***(*`x`) - :
**unifpdf***(*`x`,`a`,`b`) 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.

- :
**unifcdf***(*`x`) - :
**unifcdf***(*`x`,`a`,`b`) 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.

- :
**unifinv***(*`x`) - :
**unifinv***(*`x`,`a`,`b`) 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.

- :
**wblpdf***(*`x`) - :
**wblpdf***(*`x`,`scale`) - :
**wblpdf***(*`x`,`scale`,`shape`) Compute the probability density function (PDF) at

`x`of the Weibull distribution with scale parameter`scale`and shape parameter`shape`.This is given by

shape * scale^(-shape) * x^(shape-1) * exp (-(x/scale)^shape)

for

`x`≥ 0.Default values are

`scale`= 1,`shape`= 1.

- :
**wblcdf***(*`x`) - :
**wblcdf***(*`x`,`scale`) - :
**wblcdf***(*`x`,`scale`,`shape`) Compute the cumulative distribution function (CDF) at

`x`of the Weibull distribution with scale parameter`scale`and shape parameter`shape`.This is defined as

1 - exp (-(x/scale)^shape)

for

`x`≥ 0.Default values are

`scale`= 1,`shape`= 1.

- :
**wblinv***(*`x`) - :
**wblinv***(*`x`,`scale`) - :
**wblinv***(*`x`,`scale`,`shape`) Compute the quantile (the inverse of the CDF) at

`x`of the Weibull distribution with scale parameter`scale`and shape parameter`shape`.Default values are

`scale`= 1,`shape`= 1.

Next: Tests, Previous: Correlation and Regression Analysis, Up: Statistics [Contents][Index]