I want to find out the value of alpha and lambda where u lies between 0 and 1.
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18
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Not an answer, hopefully a step forward to clarify the question( see my comments) and to show, that the two sum's don't depend on \[Lambda]
n=5;
u = RandomReal[UniformDistribution[{0, 1}], n] // Sort;
t = -λ/Log[1 - u^(1/α)] ;
λ/t
(*{-Log[1 - 0.110733^(1/α)], -Log[1 - 0.248464^(1/α)], -Log[1 - 0.527917^(1/α)], -Log[1 - 0.626329^(1/α)], -Log[1 - 0.790666^(1/α)]}*)
That is list λ/t[[i]]
. As you might see it doesn't depend on λ
!!!
That's why the two sum's only depend on α
and therefor can't be solved for α,λ
!!!
t
andt(i)
? $\endgroup$ – Ulrich Neumann Nov 4 '20 at 16:25t
: The summation only contains quotient\ [Lambda]/t[[i]]
which by definition is a function of`u,\[Alpha]
. That's my point! $\endgroup$ – Ulrich Neumann Nov 4 '20 at 17:18