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I want to find out the value of alpha and lambda where u lies between 0 and 1.

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    $\begingroup$ Please provide some Mathematica code, thanks. What's the difference between t and t(i)? $\endgroup$ – Ulrich Neumann Nov 4 '20 at 16:25
  • $\begingroup$ Let T1, T2, . . . , Tn be a random sample of any distribution with cdf F(·), and suppose that T(i), i = 1, 2, . . . , n denotes the ordered sample. $\endgroup$ – Anu Nov 4 '20 at 16:30
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    $\begingroup$ Look at definition of t : 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
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    $\begingroup$ Sorry, I'm not a copy past machine. It's your part to provide usable code! $\endgroup$ – Ulrich Neumann Nov 6 '20 at 11:12
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    $\begingroup$ I’m voting to close this question because it is not clearly stated, the code is not present, the code presented in Wolfram Community showed no indication of debugging effort, there were two variables but only one equation, etc. $\endgroup$ – Daniel Lichtblau Nov 16 '20 at 15:30
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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 !!!

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