Description Usage Arguments Details Value References See Also Examples
The function will fit the 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 | fitBetaBin(x,obs.freq,a,b)
|
x |
vector of binomial random variables. |
obs.freq |
vector of frequencies. |
a |
single value for shape parameter alpha representing as a. |
b |
single value for shape parameter beta representing as b. |
0 < a,b
x = 0,1,2,...,n
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 fitBetaBin
gives the class format fitBB
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.
fitBB
fitted values of dBetaBin
.
NegLL
Negative Log Likelihood value.
a
estimated value for alpha parameter as a.
b
estimated value for alpha parameter as b.
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.
Young-Xu, Y. & Chan, K.A., 2008. Pooling overdispersed binomial data to estimate event rate. BMC medical research methodology, 8(1), p.58.
Available at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2538541&tool=pmcentrez&rendertype=abstract.
Trenkler, G., 1996. Continuous univariate distributions. Computational Statistics & Data Analysis, 21(1), p.119.
Available at: http://linkinghub.elsevier.com/retrieve/pii/0167947396900158.
Hughes, G., 1993. Using the Beta-Binomial Distribution to Describe Aggregated Patterns of Disease Incidence. Phytopathology, 83(9), p.759.
Available at: http://www.apsnet.org/publications/phytopathology/backissues/Documents/1993Abstracts/Phyto_83_759.htm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | 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 <- EstMLEBetaBin(No.D.D,Obs.fre.1,0.1,0.1)
bbmle::coef(parameters) #extracting the parameters a and b
aBetaBin <- bbmle::coef(parameters)[1] #assigning the parameter a
bBetaBin <- bbmle::coef(parameters)[2] #assigning the parameter b
#fitting when the random variable,frequencies,shape parameter values are given.
fitBetaBin(No.D.D,Obs.fre.1,aBetaBin,bBetaBin)
#estimating the parameters using moment generating function methods
results <- EstMGFBetaBin(No.D.D,Obs.fre.1)
results
aBetaBin1 <- results$a #assigning the estimated a
bBetaBin1 <- results$b #assigning the estimated b
#fitting when the random variable,frequencies,shape parameter values are given.
BB <- fitBetaBin(No.D.D,Obs.fre.1,aBetaBin1,bBetaBin1)
#extracting the expected frequencies
fitted(BB)
#extracting the residuals
residuals(BB)
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