Description Usage Arguments Details Value References See Also Examples
The function will fit the Gaussian Hypergeometric Generalized Beta Binomial Distribution when random variables, corresponding frequencies and shape parameters 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.
1 |
x |
vector of binomial random variables. |
obs.freq |
vector of frequencies. |
a |
single value for shape parameter alpha representing a. |
b |
single value for shape parameter beta representing b. |
c |
single value for shape parameter lambda representing c. |
0 < a,b,c
x = 0,1,2,...
obs.freq ≥ 0
NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.
The output of fitGHGBB
gives the class format fitGB
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.
fitGB
fitted values of dGHGBB
.
NegLL
Negative Loglikelihood value.
a
estimated value for alpha parameter as a.
b
estimated value for beta parameter as b.
c
estimated value for gamma parameter as c.
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.
Rodriguez-Avi, J., Conde-Sanchez, A., Saez-Castillo, A. J., & Olmo-Jimenez, M. J. (2007). A generalization of the beta-binomial distribution. Journal of the Royal Statistical Society. Series C (Applied Statistics), 56(1), 51-61.
Available at : http://dx.doi.org/10.1111/j.1467-9876.2007.00564.x
Pearson, J., 2009. Computation of Hypergeometric Functions. Transformation, (September), p.1–123.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | 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 <- EstMLEGHGBB(No.D.D,Obs.fre.1,0.1,20,1.3)
bbmle::coef(parameters) #extracting the parameters
aGHGBB <- bbmle::coef(parameters)[1] #assigning the estimated a
bGHGBB <- bbmle::coef(parameters)[2] #assigning the estimated b
cGHGBB <- bbmle::coef(parameters)[3] #assigning the estimated c
#fitting when the random variable,frequencies,shape parameter values are given.
results <- fitGHGBB(No.D.D,Obs.fre.1,aGHGBB,bGHGBB,cGHGBB)
results
#extracting the expected frequencies
fitted(results)
#extracting the residuals
residuals(results)
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