fitODBOD (version 1.5.3)

fitAddBin: Fitting the Additive Binomial Distribution when binomial random variable, frequency, probability of success and alpha are given

Description

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.

Usage

fitAddBin(x,obs.freq,p,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.

Arguments

x

vector of binomial random variables.

obs.freq

vector of frequencies.

p

single value for probability of success.

alpha

single value for alpha.

Details

$$obs.freq \ge 0$$ $$x = 0,1,2,..$$ $$0 < p < 1$$ $$-1 < alpha < 1$$

References

johnson2005univariatefitODBOD kupper1978usefitODBOD paul1985threefitODBOD morel2012overdispersionfitODBOD

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)
}