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

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.

Usage

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 NL, Kemp AW, Kotz S (2005). Univariate discrete distributions, volume 444. John Wiley and Sons. Kupper LL, Haseman JK (1978). “The use of a correlated binomial model for the analysis of certain toxicological experiments.” Biometrics, 69--76. Paul SR (1985). “A three-parameter generalization of the binomial distribution.” History and Philosophy of Logic, 14(6), 1497--1506.

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)
#> [1] 1639.987

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