Type:	Package
Title:	Finite Mixture Parametrization
Version:	0.1.3
Date:	2025-03-15
Description:	A parametrization framework for finite mixture distribution using S4 objects. Density, cumulative density, quantile and simulation functions are defined. Currently normal, Tukey g-&-h, skew-normal and skew-t distributions are well tested. The gamma, negative binomial distributions are being tested.
License:	GPL-2
Imports:	methods, goftest, sn, VGAM, param2moment, TukeyGH77
Encoding:	UTF-8
Language:	en-US
Depends:	R (≥ 4.4.0)
Suggests:	fitdistrplus, ggplot2, mixtools, mixsmsn, scales
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-03-15 18:25:19 UTC; tingtingzhan
Author:	Tingting Zhan [aut, cre], Inna Chervoneva [ctb]
Maintainer:	Tingting Zhan <tingtingzhan@gmail.com>
Repository:	CRAN
Date/Publication:	2025-03-15 22:20:06 UTC

Finite Mixture Parametrization

Description

A parametrization framework for finite mixture distribution using S4 objects.

Density, cumulative density, quantile and simulation functions are defined.

Currently normal, Tukey g-&-h, skew-normal and skew-t distributions are well tested. The gamma, negative binomial distributions are being tested.

Author(s)

Maintainer: Tingting Zhan tingtingzhan@gmail.com (ORCID)

Other contributors:

• Inna Chervoneva Inna.Chervoneva@jefferson.edu (ORCID) [contributor]

One-Sample Kolmogorov Distance

Description

To calculate the one-sample Kolmogorov distance between observations and a distribution.

Usage

Kolmogorov_dist(x, null, alternative = c("two.sided", "less", "greater"), ...)

Arguments

Details

Function Kolmogorov_dist() is different from ks.test in the following aspects

• Ties in observations are supported. The step function of empirical distribution is inspired by ecdf. This is superior than (0:(n - 1))/n in ks.test.

• Discrete distribution (with discrete observation) is supported.

• Discrete distribution (with continuous observation) is not supported yet. This will be an easy modification in future.

• Only the one-sample Kolmogorov distance, not the one-sample Kolmogorov test, is returned, to speed up the calculation.

Value

Function Kolmogorov_dist() returns a numeric scalar.

Examples

# from ?stats::ks.test
x1 = rnorm(50)
ks.test(x1+2, y = pgamma, shape = 3, rate = 2)
Kolmogorov_dist(x1+2, null = pgamma, shape = 3, rate = 2) # exactly the same

# discrete distribution
x2 <- rnbinom(n = 1e2L, size = 500, prob = .4)
suppressWarnings(ks.test(x2, y = pnbinom, size = 500, prob = .4)) # warning on ties
Kolmogorov_dist(x2, null = pnbinom, size = 500, prob = .4) # wont be the same

Maximum a Posteriori clustering

Description

..

Usage

MaP(x, dist, ...)

Arguments

Value

Function MaP() returns an integer vector.

Examples

x = rnorm(1e2L, sd = 2)
m = fmx('norm', mean = c(-1.5, 1.5), w = c(1, 2))
library(ggplot2)
ggplot() + geom_function(fun = dfmx, args = list(dist = m)) + 
  geom_point(mapping = aes(x = x, y = .05, color = factor(MaP(x, dist = m)))) + 
  labs(color = 'Maximum a Posteriori\nClustering')

Subset of Components in fmx Object

Description

Taking subset of components in fmx object

Usage

## S4 method for signature 'fmx,ANY,ANY,ANY'
x[i]

Arguments

Details

Using definitions as S3 method dispatch `[.fmx` won't work for fmx objects.

Value

An fmx object consisting of a subset of components. information about the observations (e.g. slots ⁠@data⁠ and ⁠@data.name⁠), will be lost.

Examples

(d = fmx('norm', mean = c(1, 4, 7), w = c(1, 1, 1)))
d[1:2]

Empirical Density Function

Description

..

Usage

approxdens(x, ...)

Arguments

Details

approx inside density.default

another 'layer' of approxfun

Value

Function approxdens() returns a function.

Examples

x = rnorm(1e3L)
f = approxdens(x)
f(x[1:3])

Turn Various Objects to fmx Class

Description

Turn various objects created in other R packages to fmx class.

Usage

as.fmx(x, ...)

Arguments

Details

Various mixture distribution estimates obtained from other R packages are converted to fmx class, so that we could take advantage of all methods defined for fmx objects.

Value

S3 generic function as.fmx() returns an fmx object.

Convert Normal fit from mixsmsn to fmx

Description

To convert Normal object (from package mixsmsn) to fmx class.

Usage

## S3 method for class 'Normal'
as.fmx(x, data, ...)

Arguments

Value

Function as.fmx.Normal() returns an fmx object.

Note

smsn.mix does not offer a parameter to keep the input data, as of 2021-10-06.

Examples

library(mixsmsn)
# ?smsn.mix
arg1 = c(mu = 5, sigma2 = 9, lambda = 5, nu = 5)
arg2 = c(mu = 20, sigma2 = 16, lambda = -3, nu = 5)
arg3 = c(mu = 35, sigma2 = 9, lambda = -6, nu = 5)
set.seed(120); x = rmix(n = 1e3L, p=c(.5, .2, .3), family = 'Skew.t', 
  arg = list(unname(arg1), unname(arg2), unname(arg3)))

# Normal
class(m2 <- smsn.mix(x, nu = 3, g = 3, family = 'Normal', calc.im = FALSE))
mix.hist(y = x, model = m2)
m2a = as.fmx(m2, data = x)
hist(x, freq = FALSE)
curve(dfmx(x, dist = m2a), xlim = range(x), add = TRUE)

Convert Skew.normal Object to fmx

Description

To convert Skew.normal object (from package mixsmsn) to fmx class.

Usage

## S3 method for class 'Skew.normal'
as.fmx(x, data, ...)

Arguments

Value

Function as.fmx.Skew.normal() returns an fmx object.

Note

smsn.mix does not offer a parameter to keep the input data, as of 2021-10-06.

Examples

library(mixsmsn)
# ?smsn.mix
arg1 = c(mu = 5, sigma2 = 9, lambda = 5, nu = 5)
arg2 = c(mu = 20, sigma2 = 16, lambda = -3, nu = 5)
arg3 = c(mu = 35, sigma2 = 9, lambda = -6, nu = 5)
set.seed(120); x = rmix(n = 1e3L, p=c(.5, .2, .3), family = 'Skew.t', 
  arg = list(unname(arg1), unname(arg2), unname(arg3)))

# Skew Normal
class(m1 <- smsn.mix(x, nu = 3, g = 3, family = 'Skew.normal', calc.im = FALSE))
mix.hist(y = x, model = m1)
m1a = as.fmx(m1, data = x)
(l1a = logLik(m1a))
hist(x, freq = FALSE)
curve(dfmx(x, dist = m1a), xlim = range(x), add = TRUE)

Convert Skew.t fit from mixsmsn to fmx

Description

To convert Skew.t object (from package mixsmsn) to fmx class.

Usage

## S3 method for class 'Skew.t'
as.fmx(x, data, ...)

Arguments

Value

Function as.fmx.Skew.t() returns an fmx object.

Note

smsn.mix does not offer a parameter to keep the input data, as of 2021-10-06.

Examples

# mixsmsn::smsn.mix with option `family = 'Skew.t'` is slow

library(mixsmsn)
# ?smsn.mix
arg1 = c(mu = 5, sigma2 = 9, lambda = 5, nu = 5)
arg2 = c(mu = 20, sigma2 = 16, lambda = -3, nu = 5)
arg3 = c(mu = 35, sigma2 = 9, lambda = -6, nu = 5)
set.seed(120); x = rmix(n = 1e3L, p=c(.5, .2, .3), family = 'Skew.t', 
  arg = list(unname(arg1), unname(arg2), unname(arg3)))

# Skew t
class(m3 <- smsn.mix(x, nu = 3, g = 3, family = 'Skew.t', calc.im = FALSE))
mix.hist(y = x, model = m3)
m3a = as.fmx(m3, data = x)
hist(x, freq = FALSE)
curve(dfmx(x, dist = m3a), xlim = range(x), add = TRUE)
(l3a = logLik(m3a))
stopifnot(all.equal.numeric(AIC(l3a), m3$aic), all.equal.numeric(BIC(l3a), m3$bic))

Convert fitdist Objects to fmx Class

Description

To convert fitdist objects (from package fitdistrplus) to fmx class.

Usage

## S3 method for class 'fitdist'
as.fmx(x, ...)

Arguments

Value

Function as.fmx.fitdist() returns an fmx object.

Examples

library(fitdistrplus)
# ?fitdist
data(endosulfan, package = 'fitdistrplus')
ATV <- subset(endosulfan, group == 'NonArthroInvert')$ATV
log10ATV <- log10(ATV)
fln <- fitdist(log10ATV, distr = 'norm')
(fln2 <- as.fmx(fln))
hist.default(log10ATV, freq = FALSE)
curve(dfmx(x, dist = fln2), xlim = range(log10ATV), add = TRUE)

Convert mixEM Objects to fmx Class

Description

To convert mixEM objects (from package mixtools) to fmx class.

Currently only the returned value of normalmixEM and gammamixEM are supported

Usage

## S3 method for class 'mixEM'
as.fmx(x, data = x[["x"]], ...)

Arguments

Value

Function as.fmx.mixEM() returns an fmx object.

Note

plot.mixEM not plot gammamixEM returns, as of 2022-09-19.

Examples

library(mixtools)
(wait = as.fmx(normalmixEM(faithful$waiting, k = 2)))
hist.default(faithful$waiting, freq = FALSE)
curve(dfmx(x, dist = wait), xlim = range(faithful$waiting), add = TRUE)

Convert t fit from mixsmsn to fmx

Description

To convert t object (from package mixsmsn) to fmx class.

Usage

## S3 method for class 't'
as.fmx(x, data, ...)

Arguments

Value

Function as.fmx.t() has not been completed yet

Note

smsn.mix does not offer a parameter to keep the input data, as of 2021-10-06.

Examples

library(mixsmsn)
# ?smsn.mix
arg1 = c(mu = 5, sigma2 = 9, lambda = 5, nu = 5)
arg2 = c(mu = 20, sigma2 = 16, lambda = -3, nu = 5)
arg3 = c(mu = 35, sigma2 = 9, lambda = -6, nu = 5)
set.seed(120); x = rmix(n = 1e3L, p=c(.5, .2, .3), family = 'Skew.t', 
  arg = list(unname(arg1), unname(arg2), unname(arg3)))

# t
class(m4 <- smsn.mix(x, nu = 3, g = 3, family = 't', calc.im = FALSE))
mix.hist(y = x, model = m4)
# as.fmx(m4, data = x) # not ready yet!!

Parameter Estimates of fmx object

Description

..

Usage

## S3 method for class 'fmx'
coef(object, internal = FALSE, ...)

Arguments

Details

Function coef.fmx() returns the estimates of the user-friendly parameters (parm = 'user'), or the internal/unconstrained parameters (parm = 'internal'). When the distribution has constraints on one or more parameters, function coef.fmx() does not return the estimates (which is constant 0) of the constrained parameters.

Value

Function coef.fmx() returns a numeric vector.

Confidence Interval of fmx Object

Description

...

Usage

## S3 method for class 'fmx'
confint(object, ..., level = 0.95)

Arguments

Details

Function confint.fmx() returns the Wald-type confidence intervals based on the user-friendly parameters (parm = 'user'), or the internal/unconstrained parameters (parm = 'internal'). When the distribution has constraints on one or more parameters, function confint.fmx() does not return the confident intervals of for the constrained parameters.

Value

Function confint.fmx() returns a matrix

Inverse of fmx2dbl, for internal use

Description

..

Usage

dbl2fmx(x, K, distname, ...)

Arguments

Details

Only used in downstream function QuantileGH::QLMDe and unexported function QuantileGH:::qfmx_gr, not compute intensive.

Value

Function dbl2fmx() returns a list with two elements ⁠$pars⁠ and ⁠$w⁠

Density, Distribution and Quantile of Finite Mixture Distribution

Description

Density function, distribution function, quantile function and random generation for a finite mixture distribution with normal or Tukey g-&-h components.

Usage

dfmx(
  x,
  dist,
  distname = dist@distname,
  K = dim(pars)[1L],
  pars = dist@pars,
  w = dist@w,
  ...,
  log = FALSE
)

pfmx(
  q,
  dist,
  distname = dist@distname,
  K = dim(pars)[1L],
  pars = dist@pars,
  w = dist@w,
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

qfmx(
  p,
  dist,
  distname = dist@distname,
  K = dim(pars)[1L],
  pars = dist@pars,
  w = dist@w,
  interval = qfmx_interval(dist = dist),
  ...,
  lower.tail = TRUE,
  log.p = FALSE
)

rfmx(
  n,
  dist,
  distname = dist@distname,
  K = dim(pars)[1L],
  pars = dist@pars,
  w = dist@w
)

Arguments

Details

A computational challenge in function dfmx() is when mixture density is very close to 0, which happens when the per-component log densities are negative with big absolute values. In such case, we cannot compute the log mixture densities (i.e., -Inf), for the log-likelihood using function logLik.fmx(). Our solution is to replace these -Inf log mixture densities by the weighted average (using the mixing proportions of dist) of the per-component log densities.

Function qfmx() gives the quantile function, by numerically solving pfmx. One major challenge when dealing with the finite mixture of Tukey g-&-h family distribution is that Brent–Dekker's method needs to be performed in both pGH and qfmx functions, i.e. two layers of root-finding algorithm.

Value

Function dfmx() returns a numeric vector of probability density values of an fmx object at specified quantiles x.

Function pfmx() returns a numeric vector of cumulative probability values of an fmx object at specified quantiles q.

Function qfmx() returns an unnamed numeric vector of quantiles of an fmx object, based on specified cumulative probabilities p.

Function rfmx() generates random deviates of an fmx object.

Note

Function qnorm returns an unnamed vector of quantiles, although quantile returns a named vector of quantiles.

Examples

library(ggplot2)

(e1 = fmx('norm', mean = c(0,3), sd = c(1,1.3), w = c(1, 1)))
curve(dfmx(x, dist = e1), xlim = c(-3,7))
ggplot() + geom_function(fun = dfmx, args = list(dist = e1)) + xlim(-3,7)
ggplot() + geom_function(fun = pfmx, args = list(dist = e1)) + xlim(-3,7)
hist(rfmx(n = 1e3L, dist = e1), main = '1000 obs from e1')

x = (-3):7
round(dfmx(x, dist = e1), digits = 3L)
round(p1 <- pfmx(x, dist = e1), digits = 3L)
stopifnot(all.equal.numeric(qfmx(p1, dist = e1), x, tol = 1e-4))

(e2 = fmx('GH', A = c(0,3), g = c(.2, .3), h = c(.2, .1), w = c(2, 3)))
ggplot() + geom_function(fun = dfmx, args = list(dist = e2)) + xlim(-3,7)

round(dfmx(x, dist = e2), digits = 3L)
round(p2 <- pfmx(x, dist = e2), digits = 3L)
stopifnot(all.equal.numeric(qfmx(p2, dist = e2), x, tol = 1e-4))

(e3 = fmx('GH', g = .2, h = .01)) # one-component Tukey
ggplot() + geom_function(fun = dfmx, args = list(dist = e3)) + xlim(-3,5)
set.seed(124); r1 = rfmx(1e3L, dist = e3); 
set.seed(124); r2 = TukeyGH77::rGH(n = 1e3L, g = .2, h = .01)
stopifnot(identical(r1, r2)) # but ?rfmx has much cleaner code
round(dfmx(x, dist = e3), digits = 3L)
round(p3 <- pfmx(x, dist = e3), digits = 3L)
stopifnot(all.equal.numeric(qfmx(p3, dist = e3), x, tol = 1e-4))


a1 = fmx('GH', A = c(7,9), B = c(.8, 1.2), g = c(.3, 0), h = c(0, .1), w = c(1, 1))
a2 = fmx('GH', A = c(6,9), B = c(.8, 1.2), g = c(-.3, 0), h = c(.2, .1), w = c(4, 6))
library(ggplot2)
(p = ggplot() + 
 geom_function(fun = pfmx, args = list(dist = a1), mapping = aes(color = 'g2=h1=0')) + 
 geom_function(fun = pfmx, args = list(dist = a2), mapping = aes(color = 'g2=0')) + 
 xlim(3,15) + 
 scale_y_continuous(labels = scales::percent) +
 labs(y = NULL, color = 'models') +
 coord_flip())
p + theme(legend.position = 'none')


# to use [rfmx] without \pkg{fmx}
(d = fmx(distname = 'GH', A = c(-1,1), B = c(.9,1.1), g = c(.3,-.2), h = c(.1,.05), w = c(2,3)))
d@pars
set.seed(14123); x = rfmx(n = 1e3L, dist = d)
set.seed(14123); x_raw = rfmx(n = 1e3L,
 distname = 'GH', K = 2L,
 pars = rbind(
  c(A = -1, B = .9, g = .3, h = .1),
  c(A = 1, B = 1.1, g = -.2, h = .05)
 ), 
 w = c(.4, .6)
)
stopifnot(identical(x, x_raw))

Name(s) of Formal Argument(s) of Distribution

Description

To obtain the name(s) of distribution parameter(s).

Usage

distArgs(distname)

Arguments

Value

Function distArgs() returns a character vector.

See Also

formalArgs

Distribution Type

Description

..

Usage

distType(type = c("discrete", "nonNegContinuous", "continuous"))

Arguments

Value

Function distType() returns a character vector.

Distribution Parameters that needs to have a log-transformation

Description

..

Usage

dist_logtrans(distname)

Arguments

Value

Function dist_logtrans() returns an integer scalar

Create fmx Object for Finite Mixture Distribution

Description

To create fmx object for finite mixture distribution.

Usage

fmx(distname, w = 1, ...)

Arguments

Value

Function fmx() returns an fmx object.

Examples

(e1 = fmx('norm', mean = c(0,3), sd = c(1,1.3), w = c(1, 1)))
isS4(e1) # TRUE
slotNames(e1)

(e2 = fmx('GH', A = c(0,3), g = c(.2, .3), h = c(.2, .1), w = c(2, 3)))

(e3 = fmx('GH', A = 0, g = .2, h = .2)) # one-component Tukey

fmx Class: Finite Mixture Parametrization

Description

An S4 object to specify the parameters and type of distribution of a one-dimensional finite mixture distribution.

Slots

distname

character scalar, name of parametric distribution of the mixture components. Currently, normal ('norm') and Tukey g-&-h ('GH') distributions are supported.

pars

double matrix, all distribution parameters in the mixture. Each row corresponds to one component. Each column includes the same parameters of all components. The order of rows corresponds to the (non-strictly) increasing order of the component location parameters. The columns match the formal arguments of the corresponding distribution, e.g., 'mean' and 'sd' for normal mixture, or 'A', 'B', 'g' and 'h' for Tukey g-&-h mixture.

w

numeric vector of mixing proportions that must sum to 1

data

(optional) numeric vector, the one-dimensional observations

data.name

(optional) character scalar, a human-friendly name of the observations

vcov_internal

(optional) variance-covariance matrix of the internal (i.e., unconstrained) estimates

vcov

(optional) variance-covariance matrix of the mixture distribution (i.e., constrained) estimates

Kolmogorov,CramerVonMises,KullbackLeibler

(optional) numeric scalars

Reparameterization of fmx Object

Description

To convert the parameters of fmx object into unrestricted parameters.

Usage

fmx2dbl(
  x,
  distname = x@distname,
  pars = x@pars,
  K = dim(pars)[1L],
  w = x@w,
  ...
)

Arguments

Details

For the first parameter

• A_1 \rightarrow A_1

• A_2 \rightarrow A_1 + \exp(\log(d_1))

• A_k \rightarrow A_1 + \exp(\log(d_1)) + \cdots + \exp(\log(d_{k-1}))

For mixing proportions to multinomial logits.

For 'norm': sd -> log(sd) for 'GH': ⁠B -> log(B), h -> log(h)⁠

Value

Function fmx2dbl() returns a numeric vector.

See Also

dbl2fmx()

Parameter Constraint(s) of Mixture Distribution

Description

Determine the parameter constraint(s) of a finite mixture distribution fmx, either by the value of parameters of such mixture distribution, or by a user-specified string.

Usage

fmx_constraint(
  dist,
  distname = dist@distname,
  K = dim(dist@pars)[1L],
  pars = dist@pars
)

Arguments

Value

Function fmx_constraint() returns the indices of internal parameters (only applicable to Tukey g-&-h mixture distribution, yet) to be constrained, based on the input fmx object dist.

Examples

(d0 = fmx('GH', A = c(1,4), g = c(.2,.1), h = c(.05,.1), w = c(1,1)))
(c0 = fmx_constraint(d0))
user_constraint(character(), distname = 'GH', K = 2L) # equivalent

(d1 = fmx('GH', A = c(1,4), g = c(.2,0), h = c(0,.1), w = c(1,1)))
(c1 = fmx_constraint(d1))
user_constraint(c('g2', 'h1'), distname = 'GH', K = 2L) # equivalent

(d2 = fmx('GH', A = c(1,4), g = c(.2,0), h = c(.15,.1), w = c(1,1)))
(c2 = fmx_constraint(d2))
user_constraint('g2', distname = 'GH', K = 2L) # equivalent

Diagnoses for fmx Estimates

Description

Diagnoses for fmx estimates.

Usage

Kolmogorov_fmx(object, data = object@data, ...)

KullbackLeibler_fmx(object, data = object@data, ...)

CramerVonMises_fmx(object, data = object@data, ...)

Arguments

Details

Function Kolmogorov_fmx() calculates Kolmogorov distance.

Function KullbackLeibler_fmx calculates Kullback-Leibler divergence. The R code is adapted from LaplacesDemon::KLD.

Function CramerVonMises_fmx calculates Cramer-von Mises quadratic distance (via cvm.test).

Value

Functions Kolmogorov_fmx(), KullbackLeibler_fmx(), CramerVonMises_fmx() all return numeric scalars.

See Also

dgof::cvmf.test

TeX Label (of Parameter Constraint(s)) of fmx Object

Description

Create TeX label of (parameter constraint(s)) of fmx object

Usage

getTeX(dist, print_K = FALSE)

Arguments

Value

Function getTeX() returns a character scalar (of TeX expression) of the constraint, primarily intended for end-users in plots.

Examples

(d0 = fmx('GH', A = c(1,4), g = c(.2,.1), h = c(.05,.1), w = c(1,1)))
getTeX(d0)

(d1 = fmx('GH', A = c(1,4), g = c(.2,0), h = c(0,.1), w = c(1,1)))
getTeX(d1)

(d2 = fmx('GH', A = c(1,4), g = c(.2,0), h = c(.15,.1), w = c(1,1)))
getTeX(d2)

Log-Likelihood of fitdist Object

Description

..

Usage

## S3 method for class 'fitdist'
logLik(object, ...)

Arguments

Details

Output of fitdist has elements ⁠$loglik⁠, ⁠$aic⁠ and ⁠$bic⁠, but they are simply numeric scalars. fitdistrplus:::logLik.fitdist simply returns these elements.

Value

Function logLik.fitdist() returns a logLik object, which could be further used by AIC and BIC.

(I have written to the authors)

Log-Likelihood of fmx Object

Description

..

Usage

## S3 method for class 'fmx'
logLik(object, data = object@data, ...)

Arguments

Details

Function logLik.fmx() returns a logLik object indicating the log-likelihood. An additional attribute attr(,'logl') indicates the point-wise log-likelihood, to be use in Vuong's closeness test.

Value

Function logLik.fmx() returns a logLik object with an additional attribute attr(,'logl').

Log-Likelihood of 'mixEM' Object

Description

To obtain the log-Likelihood of 'mixEM' object, based on mixtools 2020-02-05.

Usage

## S3 method for class 'mixEM'
logLik(object, ...)

Arguments

Value

Function logLik.mixEM() returns a logLik object.

Names of Distribution Parameters of 'mixEM' Object

Description

Names of distribution parameters of 'mixEM' object, based on mixtools 2020-02-05.

Usage

mixEM_pars(object)

Arguments

Value

Function mixEM_pars() returns a character vector

See Also

normalmixEM gammamixEM

Multinomial Probabilities & Logits

Description

Performs transformation between vectors of multinomial probabilities and multinomial logits.

This transformation is a generalization of plogis which converts scalar logit into probability and qlogis which converts probability into scalar logit.

Usage

qmlogis_first(p)

qmlogis_last(p)

pmlogis_first(q)

pmlogis_last(q)

Arguments

Details

Functions pmlogis_first and pmlogis_last take a length k-1 numeric vector of multinomial logits q and convert them into length k multinomial probabilities p, regarding the first or last category as reference, respectively.

Functions qmlogis_first and qmlogis_last take a length k numeric vector of multinomial probabilities p and convert them into length k-1 multinomial logits q, regarding the first or last category as reference, respectively.

Value

Functions pmlogis_first and pmlogis_last return a vector of multinomial probabilities p.

Functions qmlogis_first and qmlogis_last return a vector of multinomial logits q.

See Also

plogis qlogis

Examples

(a = qmlogis_last(c(2,5,3)))
(b = qmlogis_first(c(2,5,3)))
pmlogis_last(a)
pmlogis_first(b)

q0 = .8300964
(p1 = pmlogis_last(q0))
(q1 = qmlogis_last(p1))

# various exceptions
pmlogis_first(qmlogis_first(c(1, 0)))
pmlogis_first(qmlogis_first(c(0, 1)))
pmlogis_first(qmlogis_first(c(0, 0, 1)))
pmlogis_first(qmlogis_first(c(0, 1, 0, 0)))
pmlogis_first(qmlogis_first(c(1, 0, 0, 0)))
pmlogis_last(qmlogis_last(c(1, 0)))
pmlogis_last(qmlogis_last(c(0, 1)))
pmlogis_last(qmlogis_last(c(0, 0, 1)))
pmlogis_last(qmlogis_last(c(0, 1, 0, 0)))
pmlogis_last(qmlogis_last(c(1, 0, 0, 0)))

Creates fmx Object with Given Component-Wise Moments

Description

Creates fmx Object with Given Component-Wise Moments

Usage

moment2fmx(distname, w, ...)

Arguments

Value

Function moment2fmx() returns a fmx object.

Examples

m = c(-1.5, 1.5)
s = c(.9, 1.1)
sk = c(.2, -.3)
kt = c(.5, .75)
w = c(2, 3)
(d1 = moment2fmx(distname='GH', w=w, mean=m, sd=s, skewness=sk, kurtosis=kt))
moment_fmx(d1)
(d2 = moment2fmx(distname='st', w=w, mean=m, sd=s, skewness=sk, kurtosis=kt))
moment_fmx(d2)
library(ggplot2)
ggplot() + 
 geom_function(aes(color = 'GH'), fun = dfmx, args = list(dist=d1), n = 1001) + 
 geom_function(aes(color = 'st'), fun = dfmx, args = list(dist=d1), n = 1001) +
 xlim(-5, 6)
# two curves looks really close, but actually not identical
x = rfmx(n = 1e3L, dist = d1)
range(dfmx(x, dist = d1) - dfmx(x, dist = d2))

Moment of Each Component in an fmx Object

Description

To find moments of each component in an fmx object.

Usage

moment_fmx(object)

Arguments

Details

Function moment_fmx() calculates the moments and distribution characteristics of each mixture component of an S4 fmx object.

Value

Function moment_fmx() returns a moment object.

Examples

(d2 = fmx('GH', A = c(1,6), B = 2, g = c(0,.3), h = c(.2,0), w = c(1,2)))
moment_fmx(d2)

Number of Observations in fitdist Object

Description

..

Usage

## S3 method for class 'fitdist'
nobs(object, ...)

Arguments

Value

Function nobs.fitdist() returns an integer scalar

Number of Parameters of fmx Object

Description

..

Usage

npar.fmx(dist)

Arguments

Details

Also the degree-of-freedom in logLik, as well as stats:::AIC.logLik and stats:::BIC.logLik

Value

Function npar.fmx() returns an integer scalar.

S3 print of fmx Object

Description

..

Usage

## S3 method for class 'fmx'
print(x, ...)

Arguments

Value

Function print.fmx() returns the input fmx object invisibly.

Obtain interval for vuniroot2 for Function qfmx()

Description

Obtain interval for vuniroot2 for Function qfmx()

Usage

qfmx_interval(
  dist,
  p = c(1e-06, 1 - 1e-06),
  distname = dist@distname,
  K = dim(pars)[1L],
  pars = dist@pars,
  w = dist@w,
  ...
)

Arguments

Value

Function qfmx_interval() returns a length-2 numeric vector.

Show fmx Object

Description

Print the parameters of an fmx object and plot its density curves.

Usage

## S4 method for signature 'fmx'
show(object)

Arguments

Value

The show method for fmx object does not have a returned value.

Sort 'mixEM' Object by First Parameters

Description

To sort a 'mixEM' object by its first parameters, i.e., \mu's for normal mixture, \alpha's for \gamma-mixture, etc.

Usage

## S3 method for class 'mixEM'
sort(x, decreasing = FALSE, ...)

Arguments

Details

normalmixEM does not order the location parameter

Value

Function sort.mixEM() returns a 'mixEM' object.

See Also

sort

Sort Objects from mixsmsn by Location Parameters

Description

To sort an object returned from package mixsmsn by its location parameters

Usage

## S3 method for class 'Skew.normal'
sort(x, decreasing = FALSE, ...)

## S3 method for class 'Normal'
sort(x, decreasing = FALSE, ...)

## S3 method for class 'Skew.t'
sort(x, decreasing = FALSE, ...)

## S3 method for class 't'
sort(x, decreasing = FALSE, ...)

Arguments

Details

smsn.mix does not order the location parameter

Value

Function sort.Normal() returns a 'Normal' object.

Function sort.Skew.normal() returns a 'Skew.normal' object.

Function sort.Skew.t() returns a 'Skew.t' object.

See Also

sort

Formalize User-Specified Constraint of fmx Object

Description

Formalize user-specified constraint of fmx object

Usage

user_constraint(x, distname, K)

Arguments

Value

Function user_constraint() returns the indices of internal parameters (only applicable to Tukey's g-&-h mixture distribution, yet) to be constrained, based on the type of distribution distname, number of components K and a user-specified string (e.g., c('g2', 'h1')).

Examples

(d0 = fmx('GH', A = c(1,4), g = c(.2,.1), h = c(.05,.1), w = c(1,1)))
(c0 = fmx_constraint(d0))
user_constraint(distname = 'GH', K = 2L, x = character()) # equivalent

(d1 = fmx('GH', A = c(1,4), g = c(.2,0), h = c(0,.1), w = c(1,1)))
(c1 = fmx_constraint(d1))
user_constraint(distname = 'GH', K = 2L, x = c('g2', 'h1')) # equivalent

(d2 = fmx('GH', A = c(1,4), g = c(.2,0), h = c(.15,.1), w = c(1,1)))
(c2 = fmx_constraint(d2))
user_constraint(distname = 'GH', K = 2L, x = 'g2') # equivalent

Variance-Covariance of fmx Object

Description

..

Usage

## S3 method for class 'fmx'
vcov(object, internal = FALSE, ...)

Arguments

Details

Function vcov.fmx() returns the approximate asymptotic variance-covariance matrix of the user-friendly parameters via delta-method (parm = 'user'), or the asymptotic variance-covariance matrix of the internal/unconstrained parameters (parm = 'internal'). When the distribution has constraints on one or more parameters, function vcov.fmx() does not return the variance/covariance involving the constrained parameters.

Value

Function vcov.fmx() returns a matrix.