MLE and Bayesian estimation using R of a new probability distribution

[Malik]

How can we get the MLE of parameters of a new probability distribution using R.
How can we generate data using a new distribution using R.
Is there any expert of MCMC techniques....
I need help

[startz]

I'm not sure what you mean by a "new" probability distribution. Basically, you define a function for the likelihood and then call a function such as optim() to maximize it. There are also packages for mle that you can find with a google search.

There are a variety of functions built in to generate random numbers. For example, rnorm() generates normal random numbers.

What are you thinking about with regard to MCMC techniques?

[Malik]

Thank you sir for your kind response.
Infact I have developed a new generalized exponential distribution with two parameters. As it is a new one there is no built in package in R to find mle of parameters. Secondly I have to estimate the parameters of my distribution using MCMC techniques or any other alternative techniques...

[startz]

There would be a lot involved in MCMC, so I would start with MLE.

Write a function that takes in data and the two parameters and returns the likelihood (or the log-likelihood). You could then use optim() to maximize this. But since you only have two parameters you might just try a grid search to find the maximum.

[Malik]

This is the code to generate data by inverse function

a = 1

b = 0.5

c = 2

n = 30

x = c()

F = function(x)

(1-(exp(-bx)-exp(-ab*x))/((a-1)bx))

InvF1 = function(t) uniroot(function(x) F(x) - t, c(0,10000))$root

u = runif(n, 0, 1)

for (i in 1:n) {

x=c(x,InvF1(u[i]))

}

print(x)

But is not working for given CDF

Error is below

Error in uniroot(function(x) F(x) - t, c(0, 10000)) :

f.lower = f(lower) is NA

Secondly I require R code for MLE estimates of the parameters.
Can provide the pdf

[startz]

What is the pdf? And what are reasonable ranges for the parameters of the distribution?

[Malik]

The range of both the parameters i.e alpha and lambda and variable x is Zoro to infinity

[Malik]

Can you send me your email address and what's app number if possible please...

[startz]

Here's some code that doesn't quite work, but should get you started. Might have some typos.

# maximum likelihood for a double exponential 

logLike <- function(x,alpha,lambda){
  sum(-lambda*x - log(lambda*x^2*(1-alpha)) +
    log((alpha*lambda*x + 1)*exp(lambda*(1-alpha)*x - lambda*x - 1)))
}


# define data x around here
x <- runif(100) # just pretending

maxAlpha <- 100 # change these if unreasonable or if maximum likelihood
maxLambda <- 100 # ends up at limit
nPoints <-  100 # number of points in each direction
alpha <- seq(from=0, to= maxAlpha, length.out = nPoints) 
lambda <- seq(from=0, to= maxLambda, length.out = nPoints) 

el <- matrix(NA, nrow = length(alpha), ncol = length(lambda))

for (iAlpha in 1:length(alpha))
  for(iLambda in 1: length(lambda))
    el[iAlpha, iLambda] <- logLike(x,alpha[iAlpha],lambda[iLambda])

inds <- arrayInd(which.max(el), dim(el))

cat("mle values are: alpha=",alpha[inds[1]]," and lambda = ",lambda[inds[2]])

[startz]

I think the idea of the RStudio Community is to have public discussions where everyone can benefit.

[Malik]

Thank you very much sir
I will try it tonight