I'd be grateful if you provide me the solution or give an idea where I can find the solution of the integration. Thanks in advance.
Huda
Hello Huda Abdullah
When I have object like your, I first try to find a solution via
http://www.wolframalpha.com/examples/Math.html
If not find the easy solution via wolphram, then it give me a valid help along the Via of mathematical analysis...
Regards
Giorgio
walikum alsalam
Dear Huda
I attached for you book I think it is very good also I can help you if you until now did not solve it .
You can use some transformation to binomial series after that you can do the integration.
Hi Giorgio,
Thank you for fast answering. It's a wonderful link, but I have not found the answer yet.
Best Wishes
Huda
Dear Mundher,
I'm so grateful for the link, it's a valuable book and very important book for me, but I did not reach to the final solution yet.
Best Regards
Huda
Dear Paul,
Yes, I dont have found the answer yet.
Thank you for your valuable assistance, and I want more details.
Best Regards
Huda
Dear Huda
Pardon
have you challenge this in Wolfram Alpha?
integrate ( (x /(GAMMA (N)) * ( p t^2 )^ N ) *(1-x)^[(t^2)*p-1] *[-ln(1-x) ]^(n-1) ) dx from x=0 to 1
This is plain text input reported:
Integrate[((x/Gamma[N]) (p t^2)^N) (1 - x)^(t^2 p - 1) (-Log[1 - x])^(n - 1), {x, 0, 1}]
Solution is reported in the PNG attached file, it is a printscreen.
It say too much time, "Standard computation time exceeded...", the full solution need to buy more time..
So you can buy time or split the integral in two Integral....
Best wishes
Giorgio
Dear all,
We can simplify integration by transform logarithmic function (-log(1-x)) into power series as shown in image attached
Best regards
Now, I think, Beta distribution will be helpfull if I can transform the power series into function of x (or function of (1-x)). I'd be grateful if you can give me an idea. Thanks in advance.
Best Regards
Huda
The problem is simple. You should evaluate the integral without logarithms and then differentiate the result n-1 times with respect to p
Dear Huda,
Paul Chiou is correct. I wrote out the details for you. The change of variable is the trick. After that it's really simple.
Hello Huda
The compute of tje indefinite integral is into gratis time.
So now i attach the indefinite solution
Regards
Giorgio
Dear friends,
Thank you everyone!! I am very grateful for all your answers and your suggestions.
Dear Paul,
Of course, your answer correct. I do not know how to express my thanks. Thank you very much for giving the wonderful answer which is very important for me.
Dear Rianne,
thanks a lot for your detailed answer.
I wish you all the best
Huda
Hi,
You are right Paule. Thanks a lot.
Yes, X defined over [0,1), as you mentioned.
In fact, I have an another question and I dont know if using the power series will be helpful or another transformations should be done to solve these integrations that, shown in attached image ? Thanks in advanced.
Best Wishes for All
Huda
Dear Paul,
How wonderful are your answers!!!. Words are powerless to express my gratitude for all your help.
I'll try to find the details for your ansower of the part (1) to get the Bayes estimator for the reliability function (r(x) instead of x).
I wish you all the best
Huda
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