Nothing
R/COMPBin.R
In fitODBOD: Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD
Defines functions
summary.fitCPB
print.fitCPB
fitCOMPBin.default
fitCOMPBin
.EstMLECOMPBin
EstMLECOMPBin
NegLLCOMPBin
pCOMPBin
dCOMPBin
Documented in
dCOMPBin
EstMLECOMPBin
fitCOMPBin
NegLLCOMPBin
pCOMPBin
#' COM Poisson Binomial Distribution
#'
#' These functions provide the ability for generating probability function values and
#' cumulative probability function values for the COM Poisson Binomial Distribution.
#'
#' @usage
#' dCOMPBin(x,n,p,v)
#'
#' @param x vector of binomial random variables.
#' @param n single value for no of binomial trials.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' The probability function and cumulative function can be constructed and are denoted below
#'
#' The cumulative probability function is the summation of probability function values.
#'
#' \deqn{P_{COMPBin}(x) = \frac{{n \choose x}^v p^x (1-p)^{n-x}}{\sum_{j=0}^{n} {n \choose j}^v p^j (1-p)^{(n-j)}}}
#' \deqn{x = 0,1,2,3,...n}
#' \deqn{n = 1,2,3,...}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty }
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{dCOMPBin} gives a list format consisting
#'
#' \code{pdf} probability function values in vector form.
#'
#' \code{mean} mean of COM Poisson Binomial Distribution.
#'
#' \code{var} variance of COM Poisson Binomial Distribution.
#'
#' @references
#' Extracted from
#'
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' #plotting the random variables and probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,0.5))
#' for (i in 1:5)
#' {
#' lines(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],lwd=2.85)
#' points(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],pch=16)
#' }
#'
#' dCOMPBin(0:10,10,0.58,0.022)$pdf #extracting the pdf values
#' dCOMPBin(0:10,10,0.58,0.022)$mean #extracting the mean
#' dCOMPBin(0:10,10,0.58,0.022)$var #extracting the variance
#'
#' #plotting the random variables and cumulative probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,1))
#' for (i in 1:5)
#' {
#' lines(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],lwd=2.85)
#' points(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],pch=16)
#' }
#'
#' pCOMPBin(0:10,10,0.58,0.022) #acquiring the cumulative probability values
#'
#' @export
dCOMPBin<-function(x,n,p,v)
{
#checking if inputs consist NA(not assigned)values, infinite values or NAN(not a number)values
#if so creating an error message as well as stopping the function progress.
if(any(is.na(c(x,n,p,v))) | any(is.infinite(c(x,n,p,v))) | any(is.nan(c(x,n,p,v))) )
{
stop("NA or Infinite or NAN values in the Input")
}
else
{
#checking if at any chance the binomial random variable is greater than binomial trial value
#if so providing an error message and stopping the function progress
if(max(x) > n )
{
stop("Binomial random variable cannot be greater than binomial trial value")
}
#checking if any random variable or trial value is negative if so providig an error message
#and stopping the function progress
else if(any(x<0) | n<0)
{
stop("Binomial random variable or binomial trial value cannot be negative")
}
else
{
#checking the probability value is inbetween zero and one
if( p <= 0 | p >= 1 )
{
stop("Probability value doesnot satisfy conditions")
}
else
{
value<-NULL
#constructing the probability values for all random variables
y<-0:n
value1<-NULL
for(i in 1:length(y))
{
value1[i]<-(((choose(n,y[i]))^v)*(p^y[i])*((1-p)^(n-y[i])))/
(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))
}
check1<-sum(value1)
#checking if the sum of all probability values leads upto one
#if not providing an error message and stopping the function progress
if(check1 < 0.9999 | check1 >1.0001 | any(value1 < 0) | any(value1 >1))
{
stop("Input parameter combinations of probability of success and covariance does
not create proper probability function")
}
else
{
#for each random variable in the input vector below calculations occur
for (i in 1:length(x))
{
value[i]<-(((choose(n,x[i]))^v)*(p^x[i])*((1-p)^(n-x[i])))/
(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))
}
# generating an output in list format consisting pdf,mean and variance
return(list("pdf"=value,"mean"=sum(value1*y),
"var"=sum((y^2)*value1)-(sum(value1*y))^2))
}
}
}
}
}
#' COM Poisson Binomial Distribution
#'
#' These functions provide the ability for generating probability function values and
#' cumulative probability function values for the COM Poisson Binomial Distribution.
#'
#' @usage
#' pCOMPBin(x,n,p,v)
#'
#' @param x vector of binomial random variables.
#' @param n single value for no of binomial trials.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' The probability function and cumulative function can be constructed and are denoted below
#'
#' The cumulative probability function is the summation of probability function values.
#'
#' \deqn{P_{COMPBin}(x) = \frac{{n \choose x}^v p^x (1-p)^{n-x}}{\sum_{j=0}^{n} {n \choose j}^v p^j (1-p)^{(n-j)}}}
#' \deqn{x = 0,1,2,3,...n}
#' \deqn{n = 1,2,3,...}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty }
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{pCOMPBin} gives cumulative probability values in vector form.
#'
#' @references
#' Extracted from
#'
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' #plotting the random variables and probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,0.5))
#' for (i in 1:5)
#' {
#' lines(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],lwd=2.85)
#' points(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],pch=16)
#' }
#'
#' dCOMPBin(0:10,10,0.58,0.022)$pdf #extracting the pdf values
#' dCOMPBin(0:10,10,0.58,0.022)$mean #extracting the mean
#' dCOMPBin(0:10,10,0.58,0.022)$var #extracting the variance
#'
#' #plotting the random variables and cumulative probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,1))
#' for (i in 1:5)
#' {
#' lines(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],lwd=2.85)
#' points(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],pch=16)
#' }
#'
#' pCOMPBin(0:10,10,0.58,0.022) #acquiring the cumulative probability values
#'
#' @export
pCOMPBin<-function(x,n,p,v)
{
ans<-NULL
#for each binomial random variable in the input vector the cumulative proability function
#values are calculated
for(i in 1:length(x))
{
ans[i]<-sum(dCOMPBin(0:x[i],n,p,v)$pdf)
}
#generating an ouput vector cumulative probability function values
return(ans)
}
#' Negative Log Likelihood value of COM Poisson Binomial distribution
#'
#' This function will calculate the negative log likelihood value when the vector of binomial random
#' variables and vector of corresponding frequencies are given with the input parameters.
#'
#' @usage
#' NegLLCOMPBin(x,freq,p,v)
#'
#' @param x vector of binomial random variables.
#' @param freq vector of frequencies.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' \deqn{freq \ge 0}
#' \deqn{x = 0,1,2,..}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty}
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{NegLLCOMPBin} will produce a single numeric value.
#'
#' @references
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' No.D.D <- 0:7 #assigning the random variables
#' Obs.fre.1 <- c(47,54,43,40,40,41,39,95) #assigning the corresponding frequencies
#'
#' NegLLCOMPBin(No.D.D,Obs.fre.1,.5,.03) #acquiring the negative log likelihood value
#'
#' @export
NegLLCOMPBin<-function(x,freq,p,v)
{
#constructing the data set using the random variables vector and frequency vector
n<-max(x)
data<-rep(x,freq)
#checking if inputs consist NA(not assigned)values, infinite values or NAN(not a number)values
#if so creating an error message as well as stopping the function progress.
if(any(is.na(c(x,freq,p,v))) | any(is.infinite(c(x,freq,p,v))) |
any(is.nan(c(x,freq,p,v))) )
{
stop("NA or Infinite or NAN values in the Input")
}
else
{
#checking if any of the random variables of frequencies are less than zero if so
#creating a error message as well as stopping the function progress
if(any(c(x,freq) < 0) )
{
stop("Binomial random variable or frequency values cannot be negative")
}
#checking the probability value is inbetween zero and one or covariance is greater than zero
else if( p <= 0 | p >= 1)
{
stop("Probability value doesnot satisfy conditions")
}
else
{
value<-NULL
#constructing the probability values for all random variables
y<-0:n
value1<-NULL
for(i in 1:length(y))
{
value1[i]<-(((choose(n,y[i]))^v)*(p^y[i])*((1-p)^(n-y[i])))/
(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))
}
check1<-sum(value1)
#checking if the sum of all probability values leads upto one
#if not providing an error message and stopping the function progress
if(check1 < 0.9999 | check1 >1.0001 | any(value1 < 0) | any(value1 >1))
{
stop("Input parameter combinations of probability of success and covariance does
not create proper probability function")
}
else
{
#calculating the negative log likelihood value and representing as a single output value
return(-(v*sum(log(choose(n,data[1:sum(freq)]))) +
log(p)*sum(data[1:sum(freq)]) + log(1-p)*sum(n-data[1:sum(freq)]) -
sum(freq)*log(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))))
}
}
}
}
#' Estimating the probability of success and v parameter for COM Poisson Binomial
#' Distribution
#'
#' The function will estimate the probability of success and v parameter using the maximum log
#' likelihood method for the COM Poisson Binomial distribution when the binomial random
#' variables and corresponding frequencies are given.
#'
#' @usage
#' EstMLECOMPBin(x,freq,p,v,...)
#'
#' @param x vector of binomial random variables.
#' @param freq vector of frequencies.
#' @param p single value for probability of success.
#' @param v single value for v.
#' @param ... mle2 function inputs except data and estimating parameter.
#'
#' @details
#' \deqn{x = 0,1,2,...}
#' \deqn{freq \ge 0}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty}
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' \code{EstMLECOMPBin} here is used as a wrapper for the \code{mle2} function of \pkg{bbmle} package
#' therefore output is of class of mle2.
#'
#' @references
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' No.D.D <- 0:7 #assigning the random variables
#' Obs.fre.1 <- c(47,54,43,40,40,41,39,95) #assigning the corresponding frequencies
#'
#' #estimating the parameters using maximum log likelihood value and assigning it
#' parameters <- EstMLECOMPBin(x=No.D.D,freq=Obs.fre.1,p=0.5,v=0.1)
#'
#' bbmle::coef(parameters) #extracting the parameters
#'
#'@export
EstMLECOMPBin<-function(x,freq,p,v,...)
{
suppressWarnings2 <-function(expr, regex=character())
{
withCallingHandlers(expr, warning=function(w)
{
if (length(regex) == 1 && length(grep(regex, conditionMessage(w))))
{
invokeRestart("muffleWarning")
}
} )
}
output<-suppressWarnings2(bbmle::mle2(.EstMLECOMPBin,data=list(x=x,freq=freq),
start = list(p=p,v=v),...),"NaN")
return(output)
}
.EstMLECOMPBin<-function(x,freq,p,v)
{
#with respective to using bbmle package function mle2 there is no need impose any restrictions
#therefor the output is directly a single numeric value for the negative log likelihood value of
#COM Poisson Binomial distribution
value<-NULL
n<-max(x)
y<-0:n
data<-rep(x,freq)
return(-(v*sum(log(choose(n,data[1:sum(freq)]))) + log(p)*sum(data[1:sum(freq)]) +
log(1-p)*sum(n-data[1:sum(freq)]) - sum(freq)*log(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))))
}
#' Fitting the COM Poisson Binomial Distribution when binomial
#' random variable, frequency, probability of success and v parameter are given
#'
#' The function will fit the COM Poisson Binomial Distribution
#' when random variables, corresponding frequencies, probability of success and v parameter are given.
#' It will provide the expected frequencies, chi-squared test statistics value, p value,
#' and degree of freedom so that it can be seen if this distribution fits the data.
#'
#' @usage
#' fitCOMPBin(x,obs.freq,p,v)
#'
#' @param x vector of binomial random variables.
#' @param obs.freq vector of frequencies.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' \deqn{obs.freq \ge 0}
#' \deqn{x = 0,1,2,..}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty}
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{fitCOMPBin} gives the class format \code{fitCPB} and \code{fit} consisting a list
#'
#' \code{bin.ran.var} binomial random variables.
#'
#' \code{obs.freq} corresponding observed frequencies.
#'
#' \code{exp.freq} corresponding expected frequencies.
#'
#' \code{statistic} chi-squared test statistics.
#'
#' \code{df} degree of freedom.
#'
#' \code{p.value} probability value by chi-squared test statistic.
#'
#' \code{fitCPB} fitted probability values of \code{dCOMPBin}.
#'
#' \code{NegLL} Negative Log Likelihood value.
#'
#' \code{p} estimated probability value.
#'
#' \code{v} estimated v parameter value.
#'
#' \code{AIC} AIC value.
#'
#' \code{call} the inputs of the function.
#'
#' Methods \code{summary}, \code{print}, \code{AIC}, \code{residuals} and \code{fitted}
#' can be used to extract specific outputs.
#'
#' @references
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' No.D.D <- 0:7 #assigning the random variables
#' Obs.fre.1 <- c(47,54,43,40,40,41,39,95) #assigning the corresponding frequencies
#'
#' #estimating the parameters using maximum log likelihood value and assigning it
#' parameters <- EstMLECOMPBin(x=No.D.D,freq=Obs.fre.1,p=0.5,v=0.050)
#'
#' pCOMPBin <- bbmle::coef(parameters)[1]
#' vCOMPBin <- bbmle::coef(parameters)[2]
#'
#' #fitting when the random variable,frequencies,probability and v parameter are given
#' results <- fitCOMPBin(No.D.D,Obs.fre.1,pCOMPBin,vCOMPBin)
#' results
#'
#' #extracting the AIC value
#' AIC(results)
#'
#' #extract fitted values
#' fitted(results)
#'
#' @export
fitCOMPBin<-function(x,obs.freq,p,v)
{
#checking if inputs consist NA(not assigned)values, infinite values or NAN(not a number)values
#if so creating an error message as well as stopping the function progress.
if(any(is.na(c(x,obs.freq,p,v))) | any(is.infinite(c(x,obs.freq,p,v))) |
any(is.nan(c(x,obs.freq,p,v))) )
{
stop("NA or Infinite or NAN values in the Input")
}
else
{
est<-dCOMPBin(x,max(x),p,v)
#for given random variables and parameters calculating the estimated probability values
est.prob<-est$pdf
#using the estimated probability values the expected frequencies are calculated
exp.freq<-round((sum(obs.freq)*est.prob),2)
#chi-squared test statistics is calculated with observed frequency and expected frequency
statistic<-sum(((obs.freq-exp.freq)^2)/exp.freq)
#degree of freedom is calculated
df<-length(x)-3
#p value of chi-squared test statistic is calculated
p.value<-1-stats::pchisq(statistic,df)
#checking if df is less than or equal to zero
if(df<0 | df==0)
{
stop("Degrees of freedom cannot be less than or equal to zero")
}
#checking if any of the expected frequencies are less than five and greater than zero, if so
#a warning message is provided in interpreting the results
if(min(exp.freq)<5 && min(exp.freq) > 0)
{
message("Chi-squared approximation may be doubtful because expected frequency is less than 5")
}
#checking if expected frequency is zero, if so providing a warning message in interpreting
#the results
if(min(exp.freq)==0)
{
message("Chi-squared approximation is not suitable because expected frequency approximates to zero")
}
NegLL<-NegLLCOMPBin(x,obs.freq,p,v)
names(NegLL)<-NULL
#the final output is in a list format containing the calculated values
final<-list("bin.ran.var"=x,"obs.freq"=obs.freq,"exp.freq"=exp.freq,"statistic"=round(statistic,4),
"df"=df,"p.value"=round(p.value,4),"fitCPB"=est,
"NegLL"=NegLL,"p"=p,"v"=v,"AIC"=2*2+2*NegLL,"call"=match.call())
class(final)<-c("fitCPB","fit")
return(final)
}
}
#' @method fitCOMPBin default
#' @export
fitCOMPBin.default<-function(x,obs.freq,p,v)
{
return(fitCOMPBin(x,obs.freq,p,v))
}
#' @method print fitCPB
#' @export
print.fitCPB<-function(x,...)
{
cat("Call: \n")
print(x$call)
cat("\nChi-squared test for COM Poisson Binomial Distribution \n\t
Observed Frequency : ",x$obs.freq,"\n\t
expected Frequency : ",x$exp.freq,"\n\t
estimated p value :",x$p," ,estimated v parameter :",x$v,"\n\t
X-squared :",x$statistic," ,df :",x$df," ,p-value :",x$p.value,"\n")
}
#' @method summary fitCPB
#' @export
summary.fitCPB<-function(object,...)
{
cat("Call: \n")
print(object$call)
cat("\nChi-squared test for COM Poisson Binomial Distribution \n\t
Observed Frequency : ",object$obs.freq,"\n\t
expected Frequency : ",object$exp.freq,"\n\t
estimated p value :",object$p," ,estimated v parameter :",object$v,"\n\t
X-squared :",object$statistic," ,df :",object$df," ,p-value :",object$p.value,"\n\t
Negative Loglikehood value :",object$NegLL,"\n\t
AIC value :",object$AIC,"\n")
}
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Defines functions summary.fitCPB print.fitCPB fitCOMPBin.default fitCOMPBin .EstMLECOMPBin EstMLECOMPBin NegLLCOMPBin pCOMPBin dCOMPBin
Documented in dCOMPBin EstMLECOMPBin fitCOMPBin NegLLCOMPBin pCOMPBin
#' COM Poisson Binomial Distribution
#'
#' These functions provide the ability for generating probability function values and
#' cumulative probability function values for the COM Poisson Binomial Distribution.
#'
#' @usage
#' dCOMPBin(x,n,p,v)
#'
#' @param x vector of binomial random variables.
#' @param n single value for no of binomial trials.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' The probability function and cumulative function can be constructed and are denoted below
#'
#' The cumulative probability function is the summation of probability function values.
#'
#' \deqn{P_{COMPBin}(x) = \frac{{n \choose x}^v p^x (1-p)^{n-x}}{\sum_{j=0}^{n} {n \choose j}^v p^j (1-p)^{(n-j)}}}
#' \deqn{x = 0,1,2,3,...n}
#' \deqn{n = 1,2,3,...}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty }
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{dCOMPBin} gives a list format consisting
#'
#' \code{pdf} probability function values in vector form.
#'
#' \code{mean} mean of COM Poisson Binomial Distribution.
#'
#' \code{var} variance of COM Poisson Binomial Distribution.
#'
#' @references
#' Extracted from
#'
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' #plotting the random variables and probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,0.5))
#' for (i in 1:5)
#' {
#' lines(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],lwd=2.85)
#' points(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],pch=16)
#' }
#'
#' dCOMPBin(0:10,10,0.58,0.022)$pdf #extracting the pdf values
#' dCOMPBin(0:10,10,0.58,0.022)$mean #extracting the mean
#' dCOMPBin(0:10,10,0.58,0.022)$var #extracting the variance
#'
#' #plotting the random variables and cumulative probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,1))
#' for (i in 1:5)
#' {
#' lines(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],lwd=2.85)
#' points(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],pch=16)
#' }
#'
#' pCOMPBin(0:10,10,0.58,0.022) #acquiring the cumulative probability values
#'
#' @export
dCOMPBin<-function(x,n,p,v)
{
#checking if inputs consist NA(not assigned)values, infinite values or NAN(not a number)values
#if so creating an error message as well as stopping the function progress.
if(any(is.na(c(x,n,p,v))) | any(is.infinite(c(x,n,p,v))) | any(is.nan(c(x,n,p,v))) )
{
stop("NA or Infinite or NAN values in the Input")
}
else
{
#checking if at any chance the binomial random variable is greater than binomial trial value
#if so providing an error message and stopping the function progress
if(max(x) > n )
{
stop("Binomial random variable cannot be greater than binomial trial value")
}
#checking if any random variable or trial value is negative if so providig an error message
#and stopping the function progress
else if(any(x<0) | n<0)
{
stop("Binomial random variable or binomial trial value cannot be negative")
}
else
{
#checking the probability value is inbetween zero and one
if( p <= 0 | p >= 1 )
{
stop("Probability value doesnot satisfy conditions")
}
else
{
value<-NULL
#constructing the probability values for all random variables
y<-0:n
value1<-NULL
for(i in 1:length(y))
{
value1[i]<-(((choose(n,y[i]))^v)*(p^y[i])*((1-p)^(n-y[i])))/
(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))
}
check1<-sum(value1)
#checking if the sum of all probability values leads upto one
#if not providing an error message and stopping the function progress
if(check1 < 0.9999 | check1 >1.0001 | any(value1 < 0) | any(value1 >1))
{
stop("Input parameter combinations of probability of success and covariance does
not create proper probability function")
}
else
{
#for each random variable in the input vector below calculations occur
for (i in 1:length(x))
{
value[i]<-(((choose(n,x[i]))^v)*(p^x[i])*((1-p)^(n-x[i])))/
(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))
}
# generating an output in list format consisting pdf,mean and variance
return(list("pdf"=value,"mean"=sum(value1*y),
"var"=sum((y^2)*value1)-(sum(value1*y))^2))
}
}
}
}
}
#' COM Poisson Binomial Distribution
#'
#' These functions provide the ability for generating probability function values and
#' cumulative probability function values for the COM Poisson Binomial Distribution.
#'
#' @usage
#' pCOMPBin(x,n,p,v)
#'
#' @param x vector of binomial random variables.
#' @param n single value for no of binomial trials.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' The probability function and cumulative function can be constructed and are denoted below
#'
#' The cumulative probability function is the summation of probability function values.
#'
#' \deqn{P_{COMPBin}(x) = \frac{{n \choose x}^v p^x (1-p)^{n-x}}{\sum_{j=0}^{n} {n \choose j}^v p^j (1-p)^{(n-j)}}}
#' \deqn{x = 0,1,2,3,...n}
#' \deqn{n = 1,2,3,...}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty }
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{pCOMPBin} gives cumulative probability values in vector form.
#'
#' @references
#' Extracted from
#'
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' #plotting the random variables and probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,0.5))
#' for (i in 1:5)
#' {
#' lines(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],lwd=2.85)
#' points(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],pch=16)
#' }
#'
#' dCOMPBin(0:10,10,0.58,0.022)$pdf #extracting the pdf values
#' dCOMPBin(0:10,10,0.58,0.022)$mean #extracting the mean
#' dCOMPBin(0:10,10,0.58,0.022)$var #extracting the variance
#'
#' #plotting the random variables and cumulative probability values
#' col <- rainbow(5)
#' a <- c(0.58,0.59,0.6,0.61,0.62)
#' b <- c(0.022,0.023,0.024,0.025,0.026)
#' plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
#' ylab="Probability function values",xlim = c(0,10),ylim = c(0,1))
#' for (i in 1:5)
#' {
#' lines(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],lwd=2.85)
#' points(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],pch=16)
#' }
#'
#' pCOMPBin(0:10,10,0.58,0.022) #acquiring the cumulative probability values
#'
#' @export
pCOMPBin<-function(x,n,p,v)
{
ans<-NULL
#for each binomial random variable in the input vector the cumulative proability function
#values are calculated
for(i in 1:length(x))
{
ans[i]<-sum(dCOMPBin(0:x[i],n,p,v)$pdf)
}
#generating an ouput vector cumulative probability function values
return(ans)
}
#' Negative Log Likelihood value of COM Poisson Binomial distribution
#'
#' This function will calculate the negative log likelihood value when the vector of binomial random
#' variables and vector of corresponding frequencies are given with the input parameters.
#'
#' @usage
#' NegLLCOMPBin(x,freq,p,v)
#'
#' @param x vector of binomial random variables.
#' @param freq vector of frequencies.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' \deqn{freq \ge 0}
#' \deqn{x = 0,1,2,..}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty}
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{NegLLCOMPBin} will produce a single numeric value.
#'
#' @references
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' No.D.D <- 0:7 #assigning the random variables
#' Obs.fre.1 <- c(47,54,43,40,40,41,39,95) #assigning the corresponding frequencies
#'
#' NegLLCOMPBin(No.D.D,Obs.fre.1,.5,.03) #acquiring the negative log likelihood value
#'
#' @export
NegLLCOMPBin<-function(x,freq,p,v)
{
#constructing the data set using the random variables vector and frequency vector
n<-max(x)
data<-rep(x,freq)
#checking if inputs consist NA(not assigned)values, infinite values or NAN(not a number)values
#if so creating an error message as well as stopping the function progress.
if(any(is.na(c(x,freq,p,v))) | any(is.infinite(c(x,freq,p,v))) |
any(is.nan(c(x,freq,p,v))) )
{
stop("NA or Infinite or NAN values in the Input")
}
else
{
#checking if any of the random variables of frequencies are less than zero if so
#creating a error message as well as stopping the function progress
if(any(c(x,freq) < 0) )
{
stop("Binomial random variable or frequency values cannot be negative")
}
#checking the probability value is inbetween zero and one or covariance is greater than zero
else if( p <= 0 | p >= 1)
{
stop("Probability value doesnot satisfy conditions")
}
else
{
value<-NULL
#constructing the probability values for all random variables
y<-0:n
value1<-NULL
for(i in 1:length(y))
{
value1[i]<-(((choose(n,y[i]))^v)*(p^y[i])*((1-p)^(n-y[i])))/
(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))
}
check1<-sum(value1)
#checking if the sum of all probability values leads upto one
#if not providing an error message and stopping the function progress
if(check1 < 0.9999 | check1 >1.0001 | any(value1 < 0) | any(value1 >1))
{
stop("Input parameter combinations of probability of success and covariance does
not create proper probability function")
}
else
{
#calculating the negative log likelihood value and representing as a single output value
return(-(v*sum(log(choose(n,data[1:sum(freq)]))) +
log(p)*sum(data[1:sum(freq)]) + log(1-p)*sum(n-data[1:sum(freq)]) -
sum(freq)*log(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))))
}
}
}
}
#' Estimating the probability of success and v parameter for COM Poisson Binomial
#' Distribution
#'
#' The function will estimate the probability of success and v parameter using the maximum log
#' likelihood method for the COM Poisson Binomial distribution when the binomial random
#' variables and corresponding frequencies are given.
#'
#' @usage
#' EstMLECOMPBin(x,freq,p,v,...)
#'
#' @param x vector of binomial random variables.
#' @param freq vector of frequencies.
#' @param p single value for probability of success.
#' @param v single value for v.
#' @param ... mle2 function inputs except data and estimating parameter.
#'
#' @details
#' \deqn{x = 0,1,2,...}
#' \deqn{freq \ge 0}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty}
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' \code{EstMLECOMPBin} here is used as a wrapper for the \code{mle2} function of \pkg{bbmle} package
#' therefore output is of class of mle2.
#'
#' @references
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' No.D.D <- 0:7 #assigning the random variables
#' Obs.fre.1 <- c(47,54,43,40,40,41,39,95) #assigning the corresponding frequencies
#'
#' #estimating the parameters using maximum log likelihood value and assigning it
#' parameters <- EstMLECOMPBin(x=No.D.D,freq=Obs.fre.1,p=0.5,v=0.1)
#'
#' bbmle::coef(parameters) #extracting the parameters
#'
#'@export
EstMLECOMPBin<-function(x,freq,p,v,...)
{
suppressWarnings2 <-function(expr, regex=character())
{
withCallingHandlers(expr, warning=function(w)
{
if (length(regex) == 1 && length(grep(regex, conditionMessage(w))))
{
invokeRestart("muffleWarning")
}
} )
}
output<-suppressWarnings2(bbmle::mle2(.EstMLECOMPBin,data=list(x=x,freq=freq),
start = list(p=p,v=v),...),"NaN")
return(output)
}
.EstMLECOMPBin<-function(x,freq,p,v)
{
#with respective to using bbmle package function mle2 there is no need impose any restrictions
#therefor the output is directly a single numeric value for the negative log likelihood value of
#COM Poisson Binomial distribution
value<-NULL
n<-max(x)
y<-0:n
data<-rep(x,freq)
return(-(v*sum(log(choose(n,data[1:sum(freq)]))) + log(p)*sum(data[1:sum(freq)]) +
log(1-p)*sum(n-data[1:sum(freq)]) - sum(freq)*log(sum(((choose(n,y))^v)*(p^y)*((1-p)^(n-y))))))
}
#' Fitting the COM Poisson Binomial Distribution when binomial
#' random variable, frequency, probability of success and v parameter are given
#'
#' The function will fit the COM Poisson Binomial Distribution
#' when random variables, corresponding frequencies, probability of success and v parameter are given.
#' It will provide the expected frequencies, chi-squared test statistics value, p value,
#' and degree of freedom so that it can be seen if this distribution fits the data.
#'
#' @usage
#' fitCOMPBin(x,obs.freq,p,v)
#'
#' @param x vector of binomial random variables.
#' @param obs.freq vector of frequencies.
#' @param p single value for probability of success.
#' @param v single value for v.
#'
#' @details
#' \deqn{obs.freq \ge 0}
#' \deqn{x = 0,1,2,..}
#' \deqn{0 < p < 1}
#' \deqn{-\infty < v < +\infty}
#'
#' \strong{NOTE} : If input parameters are not in given domain conditions
#' necessary error messages will be provided to go further.
#'
#' @return
#' The output of \code{fitCOMPBin} gives the class format \code{fitCPB} and \code{fit} consisting a list
#'
#' \code{bin.ran.var} binomial random variables.
#'
#' \code{obs.freq} corresponding observed frequencies.
#'
#' \code{exp.freq} corresponding expected frequencies.
#'
#' \code{statistic} chi-squared test statistics.
#'
#' \code{df} degree of freedom.
#'
#' \code{p.value} probability value by chi-squared test statistic.
#'
#' \code{fitCPB} fitted probability values of \code{dCOMPBin}.
#'
#' \code{NegLL} Negative Log Likelihood value.
#'
#' \code{p} estimated probability value.
#'
#' \code{v} estimated v parameter value.
#'
#' \code{AIC} AIC value.
#'
#' \code{call} the inputs of the function.
#'
#' Methods \code{summary}, \code{print}, \code{AIC}, \code{residuals} and \code{fitted}
#' can be used to extract specific outputs.
#'
#' @references
#' Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type
#' generalization of the binomial distribution and its properties and applications.
#' Statistics & Probability Letters, 87, pp.158-166.
#'
#' Available at: \doi{10.1016/j.spl.2014.01.019}
#'
#' @examples
#' No.D.D <- 0:7 #assigning the random variables
#' Obs.fre.1 <- c(47,54,43,40,40,41,39,95) #assigning the corresponding frequencies
#'
#' #estimating the parameters using maximum log likelihood value and assigning it
#' parameters <- EstMLECOMPBin(x=No.D.D,freq=Obs.fre.1,p=0.5,v=0.050)
#'
#' pCOMPBin <- bbmle::coef(parameters)[1]
#' vCOMPBin <- bbmle::coef(parameters)[2]
#'
#' #fitting when the random variable,frequencies,probability and v parameter are given
#' results <- fitCOMPBin(No.D.D,Obs.fre.1,pCOMPBin,vCOMPBin)
#' results
#'
#' #extracting the AIC value
#' AIC(results)
#'
#' #extract fitted values
#' fitted(results)
#'
#' @export
fitCOMPBin<-function(x,obs.freq,p,v)
{
#checking if inputs consist NA(not assigned)values, infinite values or NAN(not a number)values
#if so creating an error message as well as stopping the function progress.
if(any(is.na(c(x,obs.freq,p,v))) | any(is.infinite(c(x,obs.freq,p,v))) |
any(is.nan(c(x,obs.freq,p,v))) )
{
stop("NA or Infinite or NAN values in the Input")
}
else
{
est<-dCOMPBin(x,max(x),p,v)
#for given random variables and parameters calculating the estimated probability values
est.prob<-est$pdf
#using the estimated probability values the expected frequencies are calculated
exp.freq<-round((sum(obs.freq)*est.prob),2)
#chi-squared test statistics is calculated with observed frequency and expected frequency
statistic<-sum(((obs.freq-exp.freq)^2)/exp.freq)
#degree of freedom is calculated
df<-length(x)-3
#p value of chi-squared test statistic is calculated
p.value<-1-stats::pchisq(statistic,df)
#checking if df is less than or equal to zero
if(df<0 | df==0)
{
stop("Degrees of freedom cannot be less than or equal to zero")
}
#checking if any of the expected frequencies are less than five and greater than zero, if so
#a warning message is provided in interpreting the results
if(min(exp.freq)<5 && min(exp.freq) > 0)
{
message("Chi-squared approximation may be doubtful because expected frequency is less than 5")
}
#checking if expected frequency is zero, if so providing a warning message in interpreting
#the results
if(min(exp.freq)==0)
{
message("Chi-squared approximation is not suitable because expected frequency approximates to zero")
}
NegLL<-NegLLCOMPBin(x,obs.freq,p,v)
names(NegLL)<-NULL
#the final output is in a list format containing the calculated values
final<-list("bin.ran.var"=x,"obs.freq"=obs.freq,"exp.freq"=exp.freq,"statistic"=round(statistic,4),
"df"=df,"p.value"=round(p.value,4),"fitCPB"=est,
"NegLL"=NegLL,"p"=p,"v"=v,"AIC"=2*2+2*NegLL,"call"=match.call())
class(final)<-c("fitCPB","fit")
return(final)
}
}
#' @method fitCOMPBin default
#' @export
fitCOMPBin.default<-function(x,obs.freq,p,v)
{
return(fitCOMPBin(x,obs.freq,p,v))
}
#' @method print fitCPB
#' @export
print.fitCPB<-function(x,...)
{
cat("Call: \n")
print(x$call)
cat("\nChi-squared test for COM Poisson Binomial Distribution \n\t
Observed Frequency : ",x$obs.freq,"\n\t
expected Frequency : ",x$exp.freq,"\n\t
estimated p value :",x$p," ,estimated v parameter :",x$v,"\n\t
X-squared :",x$statistic," ,df :",x$df," ,p-value :",x$p.value,"\n")
}
#' @method summary fitCPB
#' @export
summary.fitCPB<-function(object,...)
{
cat("Call: \n")
print(object$call)
cat("\nChi-squared test for COM Poisson Binomial Distribution \n\t
Observed Frequency : ",object$obs.freq,"\n\t
expected Frequency : ",object$exp.freq,"\n\t
estimated p value :",object$p," ,estimated v parameter :",object$v,"\n\t
X-squared :",object$statistic," ,df :",object$df," ,p-value :",object$p.value,"\n\t
Negative Loglikehood value :",object$NegLL,"\n\t
AIC value :",object$AIC,"\n")
}
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