A scalar value in the range $(0,\; 2]$ characterizing the tail behaviour of the stable distribution. You can access the alpha property using dot name assignment.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A scalar value in the range $[-1,\; 1]$ characterizing the skewness of the stable distribution. You can access the beta property using dot name assignment.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A positive scalar value characterizing the scale of the stable distribution. You can access the gam property using dot name assignment.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A scalar value characterizing the location of the stable distribution. You can access the delta property using dot name assignment.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A character vector specifying the name of the probability distribution object. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A scalar integer value specifying the number of parameters characterizing the probability distribution. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A $4\times 1$ cell array of character vectors with each element containing the name of a distribution parameter. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A $4\times 1$ cell array of character vectors with each element containing a short description of a distribution parameter. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A $4\times 1$ numeric vector containing the values of the distribution parameters, matching the order in ParameterNames. This property is read-only; use dot name assignment on the alpha, beta, gam, and delta properties.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A two-element numeric vector with the truncation interval, if the distribution is truncated. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A logical scalar that is true when the distribution is truncated. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A $4\times 4$ numeric matrix containing the variance-covariance of the distribution parameters. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A $4\times 1$ logical vector specifying which parameters are held fixed rather than estimated. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

A structure containing the data used to fit the distribution. It is empty unless the distribution was fitted with fitdist or the static fit method. This property is read-only.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: p = cdf (pd, x)

prob.StableDistribution: p = cdf (pd, x, "upper")

p = cdf (pd, x) computes the CDF of the probability distribution object, pd, evaluated at the values in x. The optional "upper" flag computes the upper tail probability.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: x = icdf (pd, p)

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

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: r = iqr (pd)

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

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: m = mean (pd)

m = mean (pd) computes the mean of the probability distribution object, pd. The mean is NaN for alpha <= 1, where it is undefined.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: m = median (pd)

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

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: nlogL = negloglik (pd)

nlogL = negloglik (pd) computes the negative loglikelihood of the probability distribution object, pd. It returns an empty value when pd is not fitted to data.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: ci = paramci (pd)

prob.StableDistribution: ci = paramci (pd, Name, Value)

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 by Name-Value pair arguments listed below.

paramci is meaningful only when pd is fitted to data, otherwise the parameter values are returned in both rows.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: y = pdf (pd, x)

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

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: plot (pd)

prob.StableDistribution: plot (pd, Name, Value)

prob.StableDistribution: h = plot (…)

plot (pd) plots the probability density function (PDF) of the probability distribution object pd. Name-value pair arguments select the plotted function and its appearance, as documented in __plot__.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: [nlogL, param] = proflik (pd, pnum)

prob.StableDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)

prob.StableDistribution: [nlogL, param] = proflik (pd, pnum, setparam)

prob.StableDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)

prob.StableDistribution: [nlogL, param] = proflik (pd)

prob.StableDistribution: [nlogL, param, other] = proflik (…)

[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 98% confidence interval and computes 101 equispaced values for the selected parameter when it is the only one being estimated, and 21 values otherwise. 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.

[nlogL, param] = proflik (pd) selects the first parameter that is not fixed.

[nlogL, param, other] = proflik (…) also returns a matrix other holding, in each row, the values of the remaining parameters that maximize the likelihood at the corresponding value of param. A fixed parameter keeps its own value.

For the stable distribution, pnum = 1 selects the tail index alpha, pnum = 2 selects the skewness beta, pnum = 3 selects the scale gam, and pnum = 4 selects the location delta.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: r = random (pd)

prob.StableDistribution: r = random (pd, rows)

prob.StableDistribution: r = random (pd, rows, cols, …)

prob.StableDistribution: r = random (pd, [sz])

r = random (pd) returns a random number from the distribution object pd, following the size conventions of stblrnd.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: s = std (pd)

s = std (pd) computes the standard deviation of the probability distribution object, pd. It is NaN for alpha < 2, where the variance is infinite.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: t = truncate (pd, lower, upper)

t = truncate (pd, lower, upper) returns the probability distribution pd truncated to the interval with lower limit lower and upper limit upper.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

prob.StableDistribution: v = var (pd)

v = var (pd) computes the variance of the probability distribution object, pd. It is NaN for alpha < 2, where the variance is infinite.

Example: 1

Create a stable distribution and plot its pdf

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");

 pd = makedist ("Stable", "alpha", 1.5, "beta", 0.5, "gam", 1, "delta", 0);

 plot (pd);

error: set: "xlim" must not be NaN

 title ("Stable distribution, alpha = 1.5, beta = 0.5");