fitCorrBin {fitODBOD} | R Documentation |
Fitting the Correlated Binomial Distribution when binomial random variable, frequency, probability of success and covariance are given
Description
The function will fit the Correlated Binomial Distribution when random variables, corresponding frequencies, probability of success and covariance 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
fitCorrBin(x,obs.freq,p,cov)
Arguments
x |
vector of binomial random variables. |
obs.freq |
vector of frequencies. |
p |
single value for probability of success. |
cov |
single value for covariance. |
Details
obs.freq \ge 0
x = 0,1,2,..
0 < p < 1
-\infty < cov < +\infty
NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.
Value
The output of fitCorrBin
gives the class format fitCB
and fit
consisting a list
bin.ran.var
binomial random variables.
obs.freq
corresponding observed frequencies.
exp.freq
corresponding expected frequencies.
statistic
chi-squared test statistics.
df
degree of freedom.
p.value
probability value by chi-squared test statistic.
corr
Correlation value.
fitCB
fitted probability values of dCorrBin
.
NegLL
Negative Log Likelihood value.
AIC
AIC value.
call
the inputs of the function.
Methods summary
, print
, AIC
, residuals
and fitted
can be used to extract specific outputs.
References
Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (Vol. 444). Hoboken, NJ: Wiley-Interscience.
L. L. Kupper, J.K.H., 1978. The Use of a Correlated Binomial Model for the Analysis of Certain Toxicological Experiments. Biometrics, 34(1), pp.69-76.
Paul, S.R., 1985. A three-parameter generalization of the binomial distribution. Communications in Statistics - Theory and Methods, 14(6), pp.1497-1506.
Available at: doi:10.1080/03610928508828990.
Jorge G. Morel and Nagaraj K. Neerchal. Overdispersion Models in SAS. SAS Institute, 2012.
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 <- EstMLECorrBin(x=No.D.D,freq=Obs.fre.1,p=0.5,cov=0.0050)
pCorrBin <- bbmle::coef(parameters)[1]
covCorrBin <- bbmle::coef(parameters)[2]
#fitting when the random variable,frequencies,probability and covariance are given
results <- fitCorrBin(No.D.D,Obs.fre.1,pCorrBin,covCorrBin)
results
#extracting the AIC value
AIC(results)
#extract fitted values
fitted(results)