### Class Definition: `GammaDistribution`

statistics: p = cdf (name, x, A)
statistics: p = cdf (name, x, A, B)
statistics: p = cdf (name, x, A, B, C)
statistics: p = cdf (…, `"upper"`)

Return the CDF of a univariate distribution evaluated at x.

`cdf` is a wrapper for the univariate cumulative distribution functions available in the statistics package. See the corresponding functions’ help to learn the signification of the parameters after x.

`p = cdf (name, x, A)` returns the CDF for the one-parameter distribution family specified by name and the distribution parameter A, evaluated at the values in x.

`p = cdf (name, x, A, B)` returns the CDF for the two-parameter distribution family specified by name and the distribution parameters A and B, evaluated at the values in x.

`p = cdf (name, x, A, B, C)` returns the CDF for the three-parameter distribution family specified by name and the distribution parameters A, B, and C, evaluated at the values in x.

`p = cdf (…, `"upper"`)` returns the complement of the CDF using an algorithm that more accurately computes the extreme upper-tail probabilities. `"upper"` can follow any of the input arguments in the previous syntaxes.

name must be a char string of the name or the abbreviation of the desired cumulative distribution function as listed in the followng table. The last column shows the number of required parameters that should be parsed after x to the desired CDF. The optional input argument `"upper"` does not count in the required number of parameters.

Distribution Name |  | Abbreviation |  | Input Parameters
--- | --- | --- | --- | ---
`"Beta"` |  | `"beta"` |  | 2
`"Binomial"` |  | `"bino"` |  | 2
`"Birnbaum-Saunders"` |  | `"bisa"` |  | 2
`"Burr"` |  | `"burr"` |  | 3
`"Cauchy"` |  | `"cauchy"` |  | 2
`"Chi-squared"` |  | `"chi2"` |  | 1
`"Extreme Value"` |  | `"ev"` |  | 2
`"Exponential"` |  | `"exp"` |  | 1
`"F-Distribution"` |  | `"f"` |  | 2
`"Gamma"` |  | `"gam"` |  | 2
`"Geometric"` |  | `"geo"` |  | 1
`"Generalized Extreme Value"` |  | `"gev"` |  | 3
`"Generalized Pareto"` |  | `"gp"` |  | 3
`"Gumbel"` |  | `"gumbel"` |  | 2
`"Half-normal"` |  | `"hn"` |  | 2
`"Hypergeometric"` |  | `"hyge"` |  | 3
`"Inverse Gaussian"` |  | `"invg"` |  | 2
`"Laplace"` |  | `"laplace"` |  | 2
`"Logistic"` |  | `"logi"` |  | 2
`"Log-Logistic"` |  | `"logl"` |  | 2
`"Lognormal"` |  | `"logn"` |  | 2
`"Nakagami"` |  | `"naka"` |  | 2
`"Negative Binomial"` |  | `"nbin"` |  | 2
`"Noncentral F-Distribution"` |  | `"ncf"` |  | 3
`"Noncentral Student T"` |  | `"nct"` |  | 2
`"Noncentral Chi-Squared"` |  | `"ncx2"` |  | 2
`"Normal"` |  | `"norm"` |  | 2
`"Poisson"` |  | `"poiss"` |  | 1
`"Rayleigh"` |  | `"rayl"` |  | 1
`"Rician"` |  | `"rice"` |  | 2
`"Student T"` |  | `"t"` |  | 1
`"location-scale T"` |  | `"tls"` |  | 3
`"Triangular"` |  | `"tri"` |  | 3
`"Discrete Uniform"` |  | `"unid"` |  | 1
`"Uniform"` |  | `"unif"` |  | 2
`"Von Mises"` |  | `"vm"` |  | 2
`"Weibull"` |  | `"wbl"` |  | 2

See also: icdf, pdf, cdf, betacdf, binocdf, bisacdf, burrcdf, cauchycdf, chi2cdf, evcdf, expcdf, fcdf, gamcdf, geocdf, gevcdf, gpcdf, gumbelcdf, hncdf, hygecdf, invgcdf, laplacecdf, logicdf, loglcdf, logncdf, nakacdf, nbincdf, ncfcdf, nctcdf, ncx2cdf, normcdf, poisscdf, raylcdf, ricecdf, tcdf, tlscdf, tricdf, unidcdf, unifcdf, vmcdf, wblcdf

Source Code: GammaDistribution

### Method: `icdf`

GammaDistribution: p = icdf (pd, p)

Compute the cumulative distribution function (CDF).

`p = icdf (pd, x)` computes the quantile (the inverse of the CDF) of the probability distribution object, pd, evaluated at the values in x.

### Method: `iqr`

GammaDistribution: r = iqr (pd)

Compute the interquartile range of a probability distribution.

`r = iqr (pd)` computes the interquartile range of the probability distribution object, pd.

### Method: `mean`

GammaDistribution: m = mean (pd)

Compute the mean of a probability distribution.

`m = mean (pd)` computes the mean of the probability distribution object, pd.

### Method: `median`

GammaDistribution: m = median (pd)

Compute the median of a probability distribution.

`m = median (pd)` computes the median of the probability distribution object, pd.

### Method: `negloglik`

GammaDistribution: nlogL = negloglik (pd)

Compute the negative loglikelihood of a probability distribution.

`m = negloglik (pd)` computes the negative loglikelihood of the probability distribution object, pd.

### Method: `paramci`

GammaDistribution: ci = paramci (pd)
GammaDistribution: ci = paramci (pd, Name, Value)

Compute the confidence intervals for probability distribution parameters.

`ci = paramci (pd)` computes the lower and upper boundaries of the 95% confidence interval for each parameter of the probability distribution object, pd.

`ci = paramci (pd, Name, Value)` computes the confidence intervals with additional options specified specified by `Name-Value` pair arguments listed below.

Name |  | Value
--- | --- | ---
`"Alpha"` |  | A scalar value in the range (0,1) specifying the significance level for the confidence interval. The default value 0.05 corresponds to a 95% confidence interval.
`"Parameter"` |  | A character vector or a cell array of character vectors specifying the parameter names for which to compute confidence intervals. By default, `paramci` computes confidence intervals for all distribution parameters.

`paramci` is meaningful only when pd is fitted to data, otherwise an empty array, `[]`, is returned.

### Method: `pdf`

GammaDistribution: y = pdf (pd, x)

Compute the probability distribution function (PDF).

`y = pdf (pd, x)` computes the PDF of the probability distribution object, pd, evaluated at the values in x.

### Method: `plot`

GammaDistribution: plot (pd)
GammaDistribution: plot (pd, Name, Value)
GammaDistribution: h = plot (…)

Plot a probability distribution object.

`plot (pd` plots a probability density function (PDF) of the probability distribution object pd. If pd contains data, which have been fitted by `fitdist`, the PDF is superimposed over a histogram of the data.

`plot (pd, Name, Value)` specifies additional options with the `Name-Value` pair arguments listed below.

| Name | Value
--- | --- | ---
`"PlotType"` |  | A character vector specifying the plot type. `"pdf"` plots the probability density function (PDF). When pd is fit to data, the PDF is superimposed on a histogram of the data. `"cdf"` plots the cumulative density function (CDF). When pd is fit to data, the CDF is superimposed over an empirical CDF. `"probability"` plots a probability plot using a CDF of the data and a CDF of the fitted probability distribution. This option is available only when pd is fitted to data.
`"Discrete"` |  | A logical scalar to specify whether to plot the PDF or CDF of a discrete distribution object as a line plot or a stem plot, by specifying `false` or `true`, respectively. By default, it is `true` for discrete distributions and `false` for continuous distributions. When pd is a continuous distribution object, option is ignored.
`"Parent"` |  | An axes graphics object for plot. If not specified, the `plot` function plots into the current axes or creates a new axes object if one does not exist.

`h = plot (…)` returns a graphics handle to the plotted objects.

### Method: `proflik`

GammaDistribution: [nlogL, param] = proflik (pd, pnum)
GammaDistribution: [nlogL, param] = proflik (pd, pnum, `"Display"`, display)
GammaDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
GammaDistribution: [nlogL, param] = proflik (pd, pnum, setparam, `"Display"`, display)

Profile likelihood function for a probability distribution object.

`[nlogL, param] = proflik (pd, pnum)` returns a vector nlogL of negative loglikelihood values and a vector param of corresponding parameter values for the parameter in the position indicated by pnum. By default, `proflik` uses the lower and upper bounds of the 95% confidence interval and computes 100 equispaced values for the selected parameter. pd must be fitted to data.

`[nlogL, param] = proflik (pd, pnum, `"Display"`, `"on"`)` also plots the profile likelihood against the default range of the selected parameter.

`[nlogL, param] = proflik (pd, pnum, setparam)` defines a user-defined range of the selected parameter.

`[nlogL, param] = proflik (pd, pnum, setparam, `"Display"`, `"on"`)` also plots the profile likelihood against the user-defined range of the selected parameter.

For the gamma distribution, `pnum = 1` selects the parameter `a` and `pnum = 2` selects the parameter b.

When opted to display the profile likelihood plot, `proflik` also plots the baseline loglikelihood computed at the lower bound of the 95% confidence interval and estimated maximum likelihood. The latter might not be observable if it is outside of the used-defined range of parameter values.

### Method: `random`

GammaDistribution: y = random (pd)
GammaDistribution: y = random (pd, rows)
GammaDistribution: y = random (pd, rows, cols, …)
GammaDistribution: y = random (pd, [sz])

Generate random arrays from the probability distribution object.

`r = random (pd)` returns a random number from the distribution object pd.

When called with a single size argument, `betarnd` returns a square matrix with the dimension specified. When called with more than one scalar argument, the first two arguments are taken as the number of rows and columns and any further arguments specify additional matrix dimensions. The size may also be specified with a row vector of dimensions, sz.

### Method: `std`

GammaDistribution: s = std (pd)

Compute the standard deviation of a probability distribution.

`s = std (pd)` computes the standard deviation of the probability distribution object, pd.

### Method: `truncate`

GammaDistribution: t = truncate (pd, lower, upper)

Truncate a probability distribution.

`t = truncate (pd)` returns a probability distribution t, which is the probability distribution pd truncated to the specified interval with lower limit, lower, and upper limit, upper. If pd is fitted to data with `fitdist`, the returned probability distribution t is not fitted, does not contain any data or estimated values, and it is as it has been created with the makedist function, but it includes the truncation interval.

### Method: `var`

GammaDistribution: v = var (pd)

Compute the variance of a probability distribution.

`v = var (pd)` computes the standard deviation of the probability distribution object, pd.