R/Kumaraswamy.R
fitKumBin.Rd
The function will fit the Kumaraswamy 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.
fitKumBin(x,obs.freq,a,b,it)
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. |
it | number of iterations to converge as a proper probability function replacing infinity. |
The output of fitKumBin
gives the class format fitKB
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.
fitKB
fitted values of dKumBin
.
NegLL
Negative Log Likelihood value.
a
estimated value for alpha parameter as a.
b
estimated value for beta parameter as b.
it
estimated it value for iterations.
AIC
AIC value.
over.dis.para
over dispersion value.
call
the inputs of the function.
Methods summary
, print
, AIC
, residuals
and fiited
can be used to
extract specific outputs.
$$0 < a,b$$ $$x = 0,1,2,...n$$ $$obs.freq \ge 0$$ $$it > 0$$
NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.
Li, X. H., Huang, Y. Y., & Zhao, X. Y. (2011). The Kumaraswamy Binomial Distribution. Chinese Journal of Applied Probability and Statistics, 27(5), 511-521.
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# NOT RUN { #estimating the parameters using maximum log likelihood value and assigning it parameters <- EstMLEKumBin(x=No.D.D,freq=Obs.fre.1,a=10.1,b=1.1,it=10000) bbmle::coef(parameters) #extracting the parameters aKumBin <- bbmle::coef(parameters)[1] #assigning the estimated a bKumBin <- bbmle::coef(parameters)[2] #assigning the estimated b itKumBin <- bbmle::coef(parameters)[3] #assigning the estimated iterations #fitting when the random variable,frequencies,shape parameter values are given. results <- fitKumBin(No.D.D,Obs.fre.1,aKumBin,bKumBin,itKumBin*100) results #extracting the expected frequencies fitted(results) #extracting the residuals residuals(results) # }