First of all thank you all for your replies. Specifically the term my term analysis. A term as

(E^(3 [Pi]^2 (16/Subscript[c, 4] + 25/Subscript[c, 5])) k^4 Subscript[c, 4] Subscript[c, 5])/(3600 [Pi]^4)

should not occur at first place it should have been mapped as per the rule: E^(X/Subscript[c, a] + Y/Subscript[c, b]) -> 2^(Subscript[n, a]/2) (( E^Subscript[T, a] Sqrt[1 + (4 X )/Subscript[c, a]] Csch[Subscript[T, a] Sqrt[1 + (4 X )/Subscript[c, a]]])/( 2 + (4 X )/Subscript[c, a] + 2 Sqrt[1 + (4 X )/Subscript[c, a]] Coth[Subscript[T, a] Sqrt[1 + (4 X )/Subscript[c, a]]]))^( Subscript[n, a]/2)* 2^( Subscript[n, b]/2) (( E^Subscript[T, b] Sqrt[1 + (4 Y )/Subscript[c, b]] Csch[Subscript[T, b] Sqrt[1 + (4 Y)/Subscript[c, b]]])/( 2 + (4 Y )/Subscript[c, b] + 2 Sqrt[1 + (4 Y )/Subscript[c, b]] Coth[Subscript[T, b] Sqrt[1 + (4 Y )/Subscript[c, b]]]))^( Subscript[n, b]/2)

which didn't happen. So I changed one of the integers like 6 to 6.0 in Subscript[G, p] -> Subscript[c, p]/(6 [Pi]^2), and the mapping went through and I can get the desired result. Thanks again.

What is surprising is one day the mapping works and other day it doesn't. Nevertheless, thanks.

p = {Subscript[T, 1] -> 5.0`20, Subscript[n, 1] -> 10.0`20, 
  Subscript[c, 1] -> 1.4`20, Subscript[T, 2] -> 5.0`20, 
  Subscript[n, 2] -> 10.0`20, Subscript[c, 2] -> 1.4`20, 
  Subscript[T, 3] -> 5.0`20, Subscript[n, 3] -> 10.0`20, 
  Subscript[c, 3] -> 1.4`20, Subscript[T, 4] -> 5.0`20, 
  Subscript[n, 4] -> 10.0`20, Subscript[c, 4] -> 1.4`20, 
  Subscript[T, 5] -> 5.0`20, Subscript[n, 5] -> 10.0`20, 
  Subscript[c, 5] -> 1.4`20, k -> 0.01`20}

Looking at it term by term:

lmn5 = List @@ termn5 /. p

I won't show the list with a lot of tiny terms along with some enormous ones, but:

Position[lmn5, Max[lmn5]]
(* {{55}} *)

So, the 55th term dominates.

termn5[[55]] /. p

(* 2.141507701982923310^363 )

Looking at it symbolically:

termn5[[55]]
(* (E^(3 \[Pi]^2 (16/Subscript[c, 4] + 25/Subscript[c, 
    5])) k^4 Subscript[c, 4] Subscript[c, 5])/(3600 \[Pi]^4) *)

Suppress the evaluation of the exponential by turning E into (undefined) e, then substitute parameters:

termn5[[55]] /. E -> e /. p

(* 5.58925700532813804710^-14 e^867.11524380999365008 )

So, you have an enormous exponential term. The exponent arises in what looks like a simple, stable calculation. Your result doesn't appear to reflect a problem in numerical calculation.

The problem is the 2.141507701982923310^363 result for termn5* at some parameter values, it should be something like .999993 (shown on old laptop, for the same set of parameters). How can I get this result on evaluating by: termn5/.{set of parameters}

So what should I do? using `20 didn't help as shown in the notebook shared now. Thanks. Pallavi

The attached notebook does not make clear what is the problem when using higher precision. It seems to give a fine numeric result. When I do the substitutions using machine numbers I see essentially the same numeric result, now with warnings that there were (apparently benign) underflows to zero.

My students old laptop gives the same output (which is more correct) but with some error message now in Mathematica 11.3. Please see the output:

It would be great help if you can suggest a solution to it in my new machine with Mathematica 11.3 installed. Thanks, Pallavi

The same happened with Mathematica 10 version and so I installed Mathematica 11.3 it too had the same problem. But worked fine in an old laptop.

I think there is no need to stay in 11.2 world, you just need to remember to ask Mathematica to use extended precision for its calculations.

Your data coincidentally were given as exact numbers (integers), so it was sufficient to simply use WorkingPrecision->20. If the data itself contains machine precision floating point numbers, it will necessary to execute epdata = SetPrecision[data, 20] and remember to use epdata in place of data.

The only important takeaway from my solution that I would recommend for you to apply going forward to replace Log[PDF[dist, x]] with LogLikelihood[dist, {x}].

Oleksandr

There are more examples, but here is my latest example with NMaximize[]:

gbdist[n, q, [Delta]_] := ParameterMixtureDistribution[BinomialDistribution[n, p], p [Distributed] BetaDistribution[ q (-1 + 1/[Delta]), ((-1 + q) (-1 + [Delta]))/[Delta]]];

loglikelihood[data, {q, [Delta]_}] := \!( *UnderoverscriptBox[([Sum]), (i = 1), (Length[data])](Log[ PDF[gbdist[data[([)(i, 1)(])], q, [Delta]], data[([)(i, 2)(])]]]))

antdata={{200, 40}, {200, 78}, {200, 97}, {200, 81}, {200, 96}}

max1 = NMaximize[{loglikelihood[antdata1, {q, [Delta]}], 0 < q < 1, 0 < [Delta] < 1}, {q, [Delta]}]

In Mathematica V 11.2: Out[26]= {-23.49, {q -> 0.370439, [Delta] -> 0.073078}}

In Mathematica V 13: General::munfl: 1.9125910^-158 (-4.167710^-216) is too small to represent as a normalized machine number; precision may be lost.

We can't help you if you don't tell use what the problem is. Just start telling us what's going on.