Solve the following equation and get one value of the result?

Questions
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1

I want to get one value of the result, which must be close to M but the result is the huge outcome.

4.nb (25.1 KB)

2

y is a list {someRandomValue}. Did you mean to do that? Once you make it a scalar (Real), M is a list of 0+i 0 so I think there’s something wrong in your equation there

3

In your second definition of M you have

Exp[Total[
  Log[1 - (1 - (1 + 2*\[Xi]*y)*Exp[-2*\[Xi]*y])^\[Mu]]^(\[Nu] - 1)]]

where Total is applied to a single expression, not to a list. The order of the operations may be wrong.

4

n is greater than 1. I just want to check the result so put n=1

5

yes sir y is a list {someRandomValue}. because n is greater than 1.

6

In your second definition for M you have the expression

((Exp[Total[
       Log[1 - (1 - (1 + 2*\[Xi]*y)*Exp[-2*\[Xi]*y])^\[Mu]]^(\[Nu] - 
        1)]] /. (\[Mu] -> RAND1)) /. (\[Nu] -> RAND2)) /. \[Xi] -> 
  RAND3

which is a tensor of rank 3. We can describe it as a 10 by 10 matrix whose entries are vectors of length 1000. Then you call Mean on {this thing}, which gives back this thing. You multiply this tensor element-by-element by a numerical vector of length 1000. I wonder if this is what you want.

7

Then how I get a single value? actually its a simulation of M’s estimator , To confirm my estimator value is right I put just n=1, for n=10 we must have 10 values and then mean of that ten values = to value of M