Question

i want R code for draw this density (pdf)

Ailamujia poisson distribution

Ailamujia logarithic distribution

Ailamujia Geometric distribution

Answer 1

First the pdf's of three distributions are defined below. The parameters are beta(>0) and lambda(0<lambda<1).

The densities when plotted for beta=2 and lambda=.5 are given below.

For query in above, comment.

R Program

beta=2
lambda=.5
f1=function(x)
{
y=4*lambda*(beta^2)*x*exp(-2*beta*x)*exp(lambda*(1+2*beta*x)*exp(-2*beta*x))/(exp(lambda)-1)
return(y)
}
f2=function(x)
{
y=4*lambda*(beta^2)*x*exp(-2*beta*x)*(-log(1-lambda)*(1-lambda*(1+2*beta*x)*exp(-2*beta*x)))^(-1)

return(y)
}
f3=function(x)
{
y=4*lambda*(beta^2)*x*exp(-2*beta*x)*(1-lambda)/(lambda*(1-lambda*(1+2*beta*x)*exp(-2*beta*x))^2)

return(y)
}

curve(f1,0,3,ylim=c(0,2.5),col="red",ylab="Density")
curve(f2,0,3,ylim=c(0,2.5),col="green",add=TRUE)
curve(f3,0,3,ylim=c(0,2.5),col="blue",add=TRUE)
legend(1.5,2.5,c("Ailamujia-Poisson","Ailamujia-Logarithmic","Ailamujia-Geometric"), col=c("red","green","blue"),lty=1)