Ajout de la fonction chisquare.test

R/cftocdf.R

@@ -6,25 +6,25 @@
 
 #' Get distribution function from characteristic function
 #' 
+#' @param grid Distribution function evaluation points
 #' @param char.fun Vectorized characteristic function
-#' @param n Amount of discretization points
-#' @param min Lower bound for distribution function
-#' @param max Upper bound for distribution function
 #' @param param Characteristic function parameters
 #' @param wmin Lower bound for transform variate
 #' @param wmax Upper bound for transform variate
 #' @return Distribution function values evaluated on [min,max] range
 #' @author François Pelletier
-cftocdf <- function(char.fun,n,min,max,param,wmin=0,wmax=50,MSwindows=FALSE)
+cftocdf <- function(grid,char.fun,...,wmin=0,wmax=50,MSwindows=FALSE)
 {
-	grid <- seq(from=min,to=max,length.out=n)
-	integrand <- function(w,x,char.fun,param,wmax=50) (1-w/wmax)*
-				Im(exp(-1i*w*x)*char.fun(w,param)) / w
+	n <- length(grid)
+	# Integral in the Gil-Pelaez Ttheorem
+	integrand <- function(w,x,char.fun,...,wmax=50) (1-w/wmax)*
+				Im(exp(-1i*w*x)*char.fun(w,...)) / w
+	# Integrate for each grid point using parallel computation if available
 	if(!MSwindows)
 	{
 		unlist(mclapply(grid,
 					function(x) 1/2-1/pi*
-								integrate(integrand,wmin,wmax,x,char.fun,param)$value))
+								integrate(integrand,wmin,wmax,x,char.fun,...)$value))
 	}
 	else
 	{
@@ -32,7 +32,7 @@ cftocdf <- function(char.fun,n,min,max,param,wmin=0,wmax=50,MSwindows=FALSE)
 		Fx <- numeric(n)
 		for(i in 1:n)
 		{
-			Fx[i] <- 1/2-1/pi*integrate(integrand,wmin,wmax,x,char.fun,param)$value
+			Fx[i] <- 1/2-1/pi*integrate(integrand,wmin,wmax,x,char.fun,...)$value
 		}
 	}
 }

R/chisquare.test.R

@@ -0,0 +1,26 @@
+# Pearson's Chi-Squared test based on the characteristic function
+# 
+# Author: François Pelletier
+###############################################################################
+
+#' Pearson's Chi-Squared test based on the characteristic function
+#' @param DATA.hist histogram object of the data
+#' @param char.fun Characteristic function
+#' @param ... Characteristic function arguments
+#' @param alpha tolerance level
+#' 
+#' @return A list containing the chi-square statistic, 
+#' degree of freedom, hypothesis reject boolean and p.value
+#' @author François Pelletier
+chisquare.test <- function(DATA.hist,char.fun,...,alpha=0.05)
+{
+	# Compute expected values for each histogram breaks using the characteristic function
+	expected <- diff(cftocdf(classes <- DATA.hist$breaks,char.fun,...)*
+					sum(observed <- DATA.hist$counts))
+	# Compute the test statistic using chi-square distribution
+	p.value <- pchisq(chisquare.stat<-sum((observed-expected)^2/expected),
+			df<-length(classes)-2,lower.tail=FALSE)
+	# Create the return list
+	list(chisquare.stat=chisquare.stat,df=df,reject=p.value<alpha,p.value=p.value)
+}
+

man/cftocdf.Rd

@@ -2,18 +2,13 @@
 \alias{cftocdf}
 \title{Get distribution function from characteristic function}
 \usage{
-cftocdf(char.fun, n, min, max, param, wmin = 0, wmax = 50,
-  MSwindows = FALSE)
+cftocdf(grid, char.fun, ..., wmin = 0, wmax = 50, MSwindows = FALSE)
 }
 \arguments{
+  \item{grid}{Distribution function evaluation points}
+
   \item{char.fun}{Vectorized characteristic function}
 
-  \item{n}{Amount of discretization points}
-
-  \item{min}{Lower bound for distribution function}
-
-  \item{max}{Upper bound for distribution function}
-
   \item{param}{Characteristic function parameters}
 
   \item{wmin}{Lower bound for transform variate}

man/chisquare.test.Rd

@@ -0,0 +1,27 @@
+\name{chisquare.test}
+\alias{chisquare.test}
+\title{Pearson's Chi-Squared test based on the characteristic function}
+\usage{
+chisquare.test(DATA.hist, char.fun, ..., alpha = 0.05)
+}
+\arguments{
+  \item{DATA.hist}{histogram object of the data}
+
+  \item{char.fun}{Characteristic function}
+
+  \item{...}{Characteristic function arguments}
+
+  \item{alpha}{tolerance level}
+}
+\value{
+A list containing the chi-square statistic, degree of
+freedom, hypothesis reject boolean and p.value
+}
+\description{
+Pearson's Chi-Squared test based on the characteristic
+function
+}
+\author{
+François Pelletier
+}
+