mpsedist | R Documentation |
Fit of univariate distributions for non-censored data using maximum product of spacing estimation (mpse), also called maximum spacing estimation.
mpsedist(
data,
distr,
start = NULL,
fix.arg = NULL,
optim.method = "default",
lower = -Inf,
upper = Inf,
custom.optim = NULL,
weights = NULL,
silent = TRUE,
gradient = NULL,
...
)
data |
A numeric vector with the observed values for non-censored data. |
distr |
A character string |
start |
A named list giving the initial values of parameters of the
named distribution or a function of data computing initial values and
returning a named list. This argument may be omitted (default) for some
distributions for which reasonable starting values are computed (see the
'details' section of |
fix.arg |
An optional named list giving the values of fixed parameters of the named distribution or a function of data computing (fixed) parameter values and returning a named list. Parameters with fixed value are thus NOT estimated. |
optim.method |
|
lower |
Left bounds on the parameters for the |
upper |
Right bounds on the parameters for the |
custom.optim |
A function carrying the optimization (see details). |
weights |
An optional vector of weights to be used in the fitting
process. Should be |
silent |
A logical to remove or show warnings when bootstrapping. |
gradient |
A function to return the gradient of the optimization
objective function for the |
... |
Further arguments passed to the |
The mpsedist
function carries out the maximum product of
spacing estimation numerically, by maximization of the arithmetic mean of
\log(F(k) - F(k-1))
.
The optimization process is the same as
mledist
, see the 'details' section of that
function.
Optionally, a vector of weights
can be used in the fitting process.
By default (when weights=NULL
), ordinary mpse is carried out,
otherwise the specified weights are used to compute a weighted arithmetic
mean.
We believe this function should be added to the package
fitdistrplus. Until it is accepted and incorporated into that
package, it will remain in the package BMT. This function is
internally called in BMTfit.mpse
.
mpsedist
returns a list with following components,
estimate |
the parameter estimates. |
convergence |
an integer code for the convergence of
|
value |
the value of the optimization objective function at the solution found. |
loglik |
the log-likelihood. |
hessian |
a symmetric matrix computed by |
optim.function |
the name of the optimization function used. |
fix.arg |
the named list giving the values of parameters of the named
distribution that must kept fixed rather than estimated by maximum
likelihood or |
optim.method |
when |
fix.arg.fun |
the function used to set the value of |
weights |
the vector of weights used in the estimation process or
|
counts |
A two-element integer vector giving the number of calls to
the log-likelihood function and its gradient respectively. This excludes
those calls needed to compute the Hessian, if requested, and any calls to
log-likelihood function to compute a finite-difference approximation to the
gradient. |
optim.message |
A character string giving any additional information
returned by the optimizer, or |
Camilo Jose Torres-Jimenez [aut,cre] cjtorresj@unal.edu.co
Based on the function mledist of the R package: fitdistrplus
Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.
Functions checkparam
and startargdefault
are needed and
were copied from the same package (fitdistrplus version: 1.0-9).
Cheng, R. and N. Amin (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society. Series B (Methodological), 394-403.
Ranneby, B. (1984). The maximum spacing method. an estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, 93-112.
mqdedist
, mledist
,
mmedist
, qmedist
,
mgedist
, and optim
.
# (1) basic fit of a normal distribution
set.seed(1234)
x1 <- rnorm(n = 100)
mean(x1); sd(x1)
mpse1 <- mpsedist(x1, "norm")
mpse1$estimate
# (2) defining your own distribution functions, here for the Gumbel
# distribution for other distributions, see the CRAN task view dedicated
# to probability distributions
dgumbel <- function(x, a, b) 1/b*exp((a-x)/b)*exp(-exp((a-x)/b))
pgumbel <- function(q, a, b) exp(-exp((a-q)/b))
qgumbel <- function(p, a, b) a-b*log(-log(p))
mpse1 <- mpsedist(x1, "gumbel", start = list(a = 10, b = 5))
mpse1$estimate
# (3) fit a discrete distribution (Poisson)
set.seed(1234)
x2 <- rpois(n = 30, lambda = 2)
mpse2 <- mpsedist(x2, "pois")
mpse2$estimate
# (4) fit a finite-support distribution (beta)
set.seed(1234)
x3 <- rbeta(n = 100, shape1 = 5, shape2 = 10)
mpse3 <- mpsedist(x3, "beta")
mpse3$estimate
# (5) fit frequency distributions on USArrests dataset.
x4 <- USArrests$Assault
mpse4pois <- mpsedist(x4, "pois")
mpse4pois$estimate
mpse4nbinom <- mpsedist(x4, "nbinom")
mpse4nbinom$estimate
# (6) weighted fit of a normal distribution
set.seed(1234)
w1 <- runif(101)
mpse1 <- mpsedist(x1, "norm", weights = w1)
mpse1$estimate
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