fitODBOD (version 1.5.3)

pLMBin: 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

pLMBin(x,n,p,phi)

Value

The output of pLMBin gives cumulative probability values in vector form.

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

$$x = 0,1,2,3,...n$$ $$n = 1,2,3,...$$ $$k = 0,1,2,...,n$$ $$0 < p < 1$$ $$0 < phi $$

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

References

elamir2013multiplicativefitODBOD

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