Is this probability function continuous?

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I have a probability function shown below, and I was wondering if it is possible to set the right side equal to 0, then take the derivative of the right side with respect to $P_j_r$ and find the global maximum. However, to do this the function should be continuous and I'm not sure if it is.



Assuming all variables other than $P_j_r$ are given constants, is this function continuous and is it possible to find the global maximum?



$$ Pr_j_r=fracy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)( sum_s=1^R y_j_sexp(frac(x_j+x_s+b*log(P_j_r))1-h))^-^hexp(I_0)+sum_r=1^Rsum_j=1^Jy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)(sum_s=1^Ry_j_sexp(fracx_j+x_r+b*log(P_j_r)1-h))^-^h $$




derivatives probability-distributions continuity




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  • I'm a little confused about why you're worrying if this function is just continous, rather than being worried for it being differentiable.
    – Ovi
    Aug 13 at 9:24










  • You can get proper formatting for functions like $exp$ and $log$ using exp and log. For operators that don't have a command of their own, you can use operatornamename.
    – joriki
    Aug 13 at 11:10














up vote
0
down vote

favorite












I have a probability function shown below, and I was wondering if it is possible to set the right side equal to 0, then take the derivative of the right side with respect to $P_j_r$ and find the global maximum. However, to do this the function should be continuous and I'm not sure if it is.



Assuming all variables other than $P_j_r$ are given constants, is this function continuous and is it possible to find the global maximum?



$$ Pr_j_r=fracy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)( sum_s=1^R y_j_sexp(frac(x_j+x_s+b*log(P_j_r))1-h))^-^hexp(I_0)+sum_r=1^Rsum_j=1^Jy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)(sum_s=1^Ry_j_sexp(fracx_j+x_r+b*log(P_j_r)1-h))^-^h $$




derivatives probability-distributions continuity




share|cite|improve this question




















  • I'm a little confused about why you're worrying if this function is just continous, rather than being worried for it being differentiable.
    – Ovi
    Aug 13 at 9:24










  • You can get proper formatting for functions like $exp$ and $log$ using exp and log. For operators that don't have a command of their own, you can use operatornamename.
    – joriki
    Aug 13 at 11:10












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have a probability function shown below, and I was wondering if it is possible to set the right side equal to 0, then take the derivative of the right side with respect to $P_j_r$ and find the global maximum. However, to do this the function should be continuous and I'm not sure if it is.



Assuming all variables other than $P_j_r$ are given constants, is this function continuous and is it possible to find the global maximum?



$$ Pr_j_r=fracy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)( sum_s=1^R y_j_sexp(frac(x_j+x_s+b*log(P_j_r))1-h))^-^hexp(I_0)+sum_r=1^Rsum_j=1^Jy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)(sum_s=1^Ry_j_sexp(fracx_j+x_r+b*log(P_j_r)1-h))^-^h $$




derivatives probability-distributions continuity




share|cite|improve this question












I have a probability function shown below, and I was wondering if it is possible to set the right side equal to 0, then take the derivative of the right side with respect to $P_j_r$ and find the global maximum. However, to do this the function should be continuous and I'm not sure if it is.



Assuming all variables other than $P_j_r$ are given constants, is this function continuous and is it possible to find the global maximum?



$$ Pr_j_r=fracy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)( sum_s=1^R y_j_sexp(frac(x_j+x_s+b*log(P_j_r))1-h))^-^hexp(I_0)+sum_r=1^Rsum_j=1^Jy_j_rexp(fracx_j+x_r+b*log(P_j_r)1-h)(sum_s=1^Ry_j_sexp(fracx_j+x_r+b*log(P_j_r)1-h))^-^h $$





derivatives probability-distributions continuity





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asked Aug 13 at 8:54









amadzebra

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  • I'm a little confused about why you're worrying if this function is just continous, rather than being worried for it being differentiable.
    – Ovi
    Aug 13 at 9:24










  • You can get proper formatting for functions like $exp$ and $log$ using exp and log. For operators that don't have a command of their own, you can use operatornamename.
    – joriki
    Aug 13 at 11:10
















  • I'm a little confused about why you're worrying if this function is just continous, rather than being worried for it being differentiable.
    – Ovi
    Aug 13 at 9:24










  • You can get proper formatting for functions like $exp$ and $log$ using exp and log. For operators that don't have a command of their own, you can use operatornamename.
    – joriki
    Aug 13 at 11:10















I'm a little confused about why you're worrying if this function is just continous, rather than being worried for it being differentiable.
– Ovi
Aug 13 at 9:24




I'm a little confused about why you're worrying if this function is just continous, rather than being worried for it being differentiable.
– Ovi
Aug 13 at 9:24












You can get proper formatting for functions like $exp$ and $log$ using exp and log. For operators that don't have a command of their own, you can use operatornamename.
– joriki
Aug 13 at 11:10




You can get proper formatting for functions like $exp$ and $log$ using exp and log. For operators that don't have a command of their own, you can use operatornamename.
– joriki
Aug 13 at 11:10















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