The function will fit the Triangular Binomial distribution when random variables, corresponding frequencies and mode parameter are given. It will provide the expected frequencies, chi-squared test statistics value, p value, degree of freedom and over dispersion value so that it can be seen if this distribution fits the data.

fitTriBin(x,obs.freq,mode)

## Arguments

x vector of binomial random variables. vector of frequencies. single value for mode.

## Value

The output of fitTriBin gives the class format fitTB 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 value.

df degree of freedom.

p.value probability value by chi-squared test statistic.

fitTB fitted probability values of dTriBin.

NegLL Negative Log Likelihood value.

mode estimated mode value.

AIC AIC value.

over.dis.para over dispersion value.

call the inputs of the function.

Methods summary, print, AIC, residuals and fitted can be used to extract specific outputs.

## Details

$$0 < mode=c < 1$$ $$x = 0,1,2,...$$ $$0 < mode < 1$$ $$obs.freq \ge 0$$

NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.

## References

Horsnell, G. (1957). Economic acceptance sampling schemes. Journal of the Royal Statistical Society, Series A, 120:148-191.

Karlis, D. & Xekalaki, E., 2008. The Polygonal Distribution. In Advances in Mathematical and Statistical Modeling. Boston: Birkhuser Boston, pp. 21-33.

Available at: http://dx.doi.org/10.1007/978-0-8176-4626-4_2.

Okagbue, H. et al., 2014. Using the Average of the Extreme Values of a Triangular Distribution for a Transformation, and Its Approximant via the Continuous Uniform Distribution. British Journal of Mathematics & Computer Science, 4(24), pp.3497-3507.

## 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

modeTriBin <- EstMLETriBin(No.D.D,Obs.fre.1)\$mode  #assigning the extracted the mode value

#fitting when the random variable,frequencies,mode value are given.
results <- fitTriBin(No.D.D,Obs.fre.1,modeTriBin)
results#> Call:
#> fitTriBin(x = No.D.D, obs.freq = Obs.fre.1, mode = modeTriBin)
#>
#> Chi-squared test for Triangular Binomial Distribution
#>
#>       Observed Frequency :  47 54 43 40 40 41 39 95
#>
#>       expected Frequency :  11.74 23.47 35.21 46.94 58.66 70.2 79.57 73.21
#>
#>       estimated Mode value: 0.944444
#>
#>       X-squared : 193.6159   ,df : 6   ,p-value : 0
#>
#>       over dispersion : 0.2308269
#extract AIC value
AIC(results)#> [1] 882.6167
#extract fitted values
fitted(results)#> [1] 11.74 23.47 35.21 46.94 58.66 70.20 79.57 73.21