dMultiBin | R Documentation |
These functions provide the ability for generating probability function values and cumulative probability function values for the Multiplicative Binomial Distribution.
dMultiBin(x,n,p,theta)
x |
vector of binomial random variables. |
n |
single value for no of binomial trials. |
p |
single value for probability of success. |
theta |
single value for theta. |
The probability function and cumulative function can be constructed and are denoted below
The cumulative probability function is the summation of probability function values.
P_{MultiBin}(x)= {n \choose x} p^x (1-p)^{n-x} \frac{(theta^{x(n-x)}}{f(p,theta,n)}
here f(p,theta,n) is
f(p,theta,n)= ∑_{k=0}^{n} {n \choose k} p^k (1-p)^{n-k} (theta^{k(n-k)} )
x = 0,1,2,3,...n
n = 1,2,3,...
k = 0,1,2,...,n
0 < p < 1
0 < theta
NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.
The output of dMultiBin
gives a list format consisting
pdf
probability function values in vector form.
mean
mean of Multiplicative Binomial Distribution.
var
variance of Multiplicative Binomial Distribution.
Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (Vol. 444). Hoboken, NJ: Wiley-Interscience.
L. L. Kupper, J.K.H., 1978. The Use of a Correlated Binomial Model for the Analysis of Certain Toxicological Experiments. Biometrics, 34(1), pp.69-76.
Paul, S.R., 1985. A three-parameter generalization of the binomial distribution. Communications in Statistics - Theory and Methods, 14(6), pp.1497-1506.
Available at: doi: 10.1080/03610928508828990.
#plotting the random variables and probability values col <- rainbow(5) a <- c(0.58,0.59,0.6,0.61,0.62) b <- c(0.022,0.023,0.024,0.025,0.026) plot(0,0,main="Multiplicative binomial probability function graph",xlab="Binomial random variable", ylab="Probability function values",xlim = c(0,10),ylim = c(0,0.5)) for (i in 1:5) { lines(0:10,dMultiBin(0:10,10,a[i],1+b[i])$pdf,col = col[i],lwd=2.85) points(0:10,dMultiBin(0:10,10,a[i],1+b[i])$pdf,col = col[i],pch=16) } dMultiBin(0:10,10,.58,10.022)$pdf #extracting the pdf values dMultiBin(0:10,10,.58,10.022)$mean #extracting the mean dMultiBin(0:10,10,.58,10.022)$var #extracting the variance #plotting random variables and cumulative probability values col <- rainbow(5) a <- c(0.58,0.59,0.6,0.61,0.62) b <- c(0.022,0.023,0.024,0.025,0.026) plot(0,0,main="Multiplicative binomial probability function graph",xlab="Binomial random variable", ylab="Probability function values",xlim = c(0,10),ylim = c(0,1)) for (i in 1:5) { lines(0:10,pMultiBin(0:10,10,a[i],1+b[i]),col = col[i],lwd=2.85) points(0:10,pMultiBin(0:10,10,a[i],1+b[i]),col = col[i],pch=16) } pMultiBin(0:10,10,.58,10.022) #acquiring the cumulative probability values
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