dLMBin: Lovinson Multiplicative Binomial Distribution

In fitODBOD: Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD

Lovinson Multiplicative Binomial Distribution

Description

These functions provide the ability for generating probability function values and cumulative probability function values for the Lovinson Multiplicative Binomial Distribution.

Usage

dLMBin(x,n,p,phi)

Arguments

x	vector of binomial random variables.
n	single value for no of binomial trials.
p	single value for probability of success.
phi	single value for phi.

Details

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_{LMBin}(x)= {n \choose x} p^x (1-p)^{n-x} \frac{(phi^{x(n-x)}}{f(p,phi,n)}

here f(p,phi,n) is

f(p,phi,n)= ∑_{k=0}^{n} {n \choose k} p^k (1-p)^{n-k} (phi^{k(n-k)} )

x = 0,1,2,3,...n

n = 1,2,3,...

k = 0,1,2,...,n

0 < p < 1

0 < phi

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

Value

The output of dLMBin gives a list format consisting

pdf probability function values in vector form.

mean mean of Lovinson Multiplicative Binomial Distribution.

var variance of Lovinson Multiplicative Binomial Distribution.

References

Elamir, E.A., 2013. Multiplicative-Binomial Distribution: Some Results on Characterization, Inference and Random Data Generation. Journal of Statistical Theory and Applications, 12(1), pp.92-105.

Examples

#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="Lovinson 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,dLMBin(0:10,10,a[i],1+b[i])$pdf,col = col[i],lwd=2.85)
points(0:10,dLMBin(0:10,10,a[i],1+b[i])$pdf,col = col[i],pch=16)
}

dLMBin(0:10,10,.58,10.022)$pdf   #extracting the pdf values
dLMBin(0:10,10,.58,10.022)$mean   #extracting the mean
dLMBin(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="Lovinson 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,pLMBin(0:10,10,a[i],1+b[i]),col = col[i],lwd=2.85)
points(0:10,pLMBin(0:10,10,a[i],1+b[i]),col = col[i],pch=16)
}

pLMBin(0:10,10,.58,10.022)     #acquiring the cumulative probability values

fitODBOD documentation built on Jan. 15, 2023, 5:11 p.m.