tLocationScaleDistribution
"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 (…, returns the complement of the
CDF using an algorithm that more accurately computes the extreme upper-tail
probabilities. "upper")"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: tLocationScaleDistribution
icdf
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.
iqr
Compute the interquartile range of a probability distribution.
r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.
mean
Compute the mean of a probability distribution.
m = mean (pd) computes the mean of the probability
distribution object, pd.
median
Compute the median of a probability distribution.
m = median (pd) computes the median of the probability
distribution object, pd.
negloglik
Compute the negative loglikelihood of a probability distribution.
m = negloglik (pd) computes the negative loglikelihood
of the probability distribution object, pd.
paramci
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 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.
pdf
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.
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.
proflik
"Display", display)"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,
also plots the profile likelihood
against the default range of the selected parameter.
"Display", "on")
[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.
[nlogL, param] = proflik (pd, pnum,
setparam, also plots the profile
likelihood against the user-defined range of the selected parameter.
"Display", "on")
For the location-scale T distribution, pnum = 1 selects the
parameter mu, pnum = 2 selects the parameter
sigma, and pnum = 3 selects the parameter nu.
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.
random
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.
std
Compute the standard deviation of a probability distribution.
s = std (pd) computes the standard deviation of the
probability distribution object, pd.
tLocationScaleDistribution
Compute the variance of a probability distribution.
v = var (pd) computes the standard deviation of the
probability distribution object, pd.
truncate
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.
var
Compute the variance of a probability distribution.
v = var (pd) computes the standard deviation of the
probability distribution object, pd.