Fitting the Additive Binomial Distribution when binomial random variable, frequency, probability of success and alpha are given
Source:R/AddBin.R
fitAddBin.Rd
The function will fit the Additive Binomial distribution when random variables, corresponding frequencies, probability of success and alpha are given. It will provide the expected frequencies, chi-squared test statistics value, p value, and degree of freedom value so that it can be seen if this distribution fits the data.
Arguments
- x
vector of binomial random variables.
- obs.freq
vector of frequencies.
- p
single value for probability of success.
- alpha
single value for alpha.
Value
The output of fitAddBin
gives the class format fitAB
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.
fitAB
fitted probability values of dAddBin
.
NegLL
Negative Log Likelihood value.
p
estimated probability value.
alpha
estimated alpha parameter 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 the frequencies
if (FALSE) {
#assigning the estimated probability value
paddbin <- EstMLEAddBin(No.D.D,Obs.fre.1)$p
#assigning the estimated alpha value
alphaaddbin <- EstMLEAddBin(No.D.D,Obs.fre.1)$alpha
#fitting when the random variable,frequencies,probability and alpha are given
results <- fitAddBin(No.D.D,Obs.fre.1,paddbin,alphaaddbin)
results
#extracting the AIC value
AIC(results)
#extract fitted values
fitted(results)
}