univMoTBF {MoTBFs}

Fitting MoTBFs

Description

Function for fitting univariate mixture of truncated basis functions. Least square optimization is used to minimize the quadratic error between the empirical cumulative distribution and the estimated one.

Usage

univMoTBF(
  data,
  POTENTIAL_TYPE,
  evalRange = NULL,
  nparam = NULL,
  maxParam = NULL
)

Arguments

data

A "numeric" vector.

POTENTIAL_TYPE

A "character" string specifying the potential type, must be either "MOP" or "MTE".

evalRange

A "numeric" vector that specifies the domain over which the model will be fitted. By default, it is NULL and the function is defined over the complete data range.

nparam

The exact number of basis functions to be used. By default, it is NULL and the best MoTBF is fitted taking into account the Bayesian information criterion (BIC) to score and select the functions. It evaluates the next two functions and, if the BIC value does not improve, the function with the best BIC score so far is returned.

maxParam

A "numeric" value which indicates the maximum number of coefficients in the function. By default, it is NULL; otherwise, the function which gets the best BIC score with at most this number of parameters is returned.

Value

univMoTBF() returns an object of class "motbf". This object is a list containing several elements, including its mathematical expression and other hidden elements related to the learning task. The processing time is one of the values returned by this function and it can be extracted by $Time. Although the learning process is always the same for a particular data sample, the processing can vary inasmuch as it depends on the CPU.

Examples

## 1. EXAMPLE
## Data
X <- rnorm(5000)

## Learning
f1 <- univMoTBF(X, POTENTIAL_TYPE = "MTE"); f1
f2 <- univMoTBF(X, POTENTIAL_TYPE = "MOP"); f2

## Plots
hist(X, prob = TRUE, main = "")
plot(f1, xlim = range(X), col = 1, add = TRUE)
plot(f2, xlim = range(X), col = 2, add = TRUE)

## Data test
Xtest <- rnorm(1000)
## Filtered data test
Xtest <- Xtest[Xtest>=min(X) & Xtest<=max(X)]

## Log-likelihood
sum(log(as.function(f1)(Xtest)))
sum(log(as.function(f2)(Xtest)))

## 2. EXAMPLE
## Data
X <- rchisq(5000, df = 5)

## Learning
f1 <- univMoTBF(X, POTENTIAL_TYPE = "MTE", nparam = 11); f1
f2 <- univMoTBF(X, POTENTIAL_TYPE = "MOP", maxParam = 10); f2

## Plots
hist(X, prob = TRUE, main = "")
plot(f1, xlim = range(X), col = 3, add = TRUE)
plot(f2, xlim = range(X), col = 4, add = TRUE)

## Data test
Xtest <- rchisq(1000, df = 5)
## Filtered data test
Xtest <- Xtest[Xtest>=min(X) & Xtest<=max(X)]

## Log-likelihood
sum(log(as.function(f1)(Xtest)))
sum(log(as.function(f2)(Xtest)))