Fitting the Multiplicative Binomial Distribution when binomial random variable, frequency, probability of success and theta parameter are given

Source: R/MultiBin.R

The function will fit the Multiplicative Binomial distribution when random variables, corresponding frequencies, probability of success and theta parameter 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.

fitMultiBin(x,obs.freq,p,theta)

Arguments

x

vector of binomial random variables.
obs.freq

vector of frequencies.
p

single value for probability of success.
theta

single value for theta parameter.

Value

The output of fitMultiBin gives the class format fitMuB 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.

fitMuB fitted probability values of dMultiBin.

NegLL Negative Log Likelihood value.

p estimated probability value.

theta estimated theta 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.

Details

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

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: http://www.tandfonline.com/doi/abs/10.1080/03610928508828990.

See also

mle2

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 <- EstMLEMultiBin(x=No.D.D,freq=Obs.fre.1,p=0.1,theta=.3)

pMultiBin <- bbmle::coef(parameters)[1]    #assigning the estimated probability value
thetaMultiBin <- bbmle::coef(parameters)[2]  #assigning the estimated theta value

#fitting when the random variable,frequencies,probability and theta are given
results <- fitMultiBin(No.D.D,Obs.fre.1,pMultiBin,thetaMultiBin)
results
#> Call: 
#> fitMultiBin(x = No.D.D, obs.freq = Obs.fre.1, p = pMultiBin, 
#>     theta = thetaMultiBin)
#> 
#> Chi-squared test for Multiplicative Binomial Distribution 
#> 	
#>       Observed Frequency :  47 54 43 40 40 41 39 95 
#> 	
#>       expected Frequency :  54.3 49.54 38.86 33.97 35.74 45.26 63.86 77.48 
#> 	
#>       estimated p value : 0.5126962  ,estimated theta parameter : 0.7060546 
#> 	
#>       X-squared : 17.4425   ,df : 5   ,p-value : 0.0037 

#extracting the AIC value
AIC(results)
#>        p 
#> 821.9933 

#extract fitted values
fitted(results)
#> [1] 54.30 49.54 38.86 33.97 35.74 45.26 63.86 77.48