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solve a system of equation numericlly

March 16, 2017, 4:27 am
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i want to solve the system of equation ( 1 )  , (2)  ,  (3)   under the assumation that x , y have the CDF in (4)  ,  (5)
 

> 

diff(L(lambda[1], lambda[2], alpha), lambda[1]) = n/lambda[1]+sum(x[i], i = 1 .. n)-(sum(2*x[i]*exp(lambda[1])/(exp(x__i*`λ__1`)-1+alpha), i = 1 .. n))

diff(L(lambda[1], lambda[2], alpha), lambda[1]) = n/lambda[1]+sum(x[i], i = 1 .. n)-(sum(2*x[i]*exp(lambda[1])/(exp(x__i*`λ__1`)-1+alpha), i = 1 .. n))

(1)
> 

diff(L(lambda[1], lambda[2], alpha), lambda[2]) = m/lambda[2]+sum(y[j], j = 1 .. m)-(sum(2*y[j]*exp(lambda[2])/(exp(y__j*`λ__2`)-1+alpha), j = 1 .. m))

diff(L(lambda[1], lambda[2], alpha), lambda[2]) = m/lambda[2]+sum(y[j], j = 1 .. m)-(sum(2*y[j]*exp(lambda[2])/(exp(y__j*`λ__2`)-1+alpha), j = 1 .. m))

(2)
> 

diff(L(lambda[1], lambda[2], alpha), alpha) = (n+m)/alpha-(sum(2/(exp(x[i]*`λ__1`)-1+alpha), i = 1 .. n))-(sum(2/(exp(y[j]*`λ__2`)-1+alpha), j = 1 .. m))

diff(L(lambda[1], lambda[2], alpha), alpha) = (n+m)/alpha-(sum(2/(exp(x[i]*`λ__1`)-1+alpha), i = 1 .. n))-(sum(2/(exp(y[j]*`λ__2`)-1+alpha), j = 1 .. m))

(3)
> 

G(x, lambda[1], alpha) = 1-alpha/(exp(lambda[1]*x)-1+alpha)

G(x, lambda[1], alpha) = 1-alpha/(exp(lambda[1]*x)-1+alpha)

(4)
> 

G(y, lambda[2], alpha) = 1-alpha/(exp(lambda[2]*x)-1+alpha)

G(y, lambda[2], alpha) = 1-alpha/(exp(lambda[2]*x)-1+alpha)

(5)
> 

``

> 

``


 

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