Non-monotonic transformation of Uniform distribution and derivative
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Let $Xsim Uniform[0,1]$ and $z:[0,1]rightarrow[0,1]$ be a non-monotonic function (but with very nice features such as continuity, differentiability, etc).
If a function $alpha$ is defined to be $$alpha(t)=P[z(X)leq t],$$ Is there anyway that we can get a closed form representaiton of $alpha'(t)$?
transformation uniform-distribution
asked 8 hours ago
Greenteamaniac
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up vote
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Let $Xsim Uniform[0,1]$ and $z:[0,1]rightarrow[0,1]$ be a non-monotonic function (but with very nice features such as continuity, differentiability, etc).
If a function $alpha$ is defined to be $$alpha(t)=P[z(X)leq t],$$ Is there anyway that we can get a closed form representaiton of $alpha'(t)$?
transformation uniform-distribution
asked 8 hours ago
Greenteamaniac
134
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $Xsim Uniform[0,1]$ and $z:[0,1]rightarrow[0,1]$ be a non-monotonic function (but with very nice features such as continuity, differentiability, etc).
If a function $alpha$ is defined to be $$alpha(t)=P[z(X)leq t],$$ Is there anyway that we can get a closed form representaiton of $alpha'(t)$?
transformation uniform-distribution
asked 8 hours ago
Greenteamaniac
134
Let $Xsim Uniform[0,1]$ and $z:[0,1]rightarrow[0,1]$ be a non-monotonic function (but with very nice features such as continuity, differentiability, etc).
If a function $alpha$ is defined to be $$alpha(t)=P[z(X)leq t],$$ Is there anyway that we can get a closed form representaiton of $alpha'(t)$?
transformation uniform-distribution
transformation uniform-distribution
asked 8 hours ago
Greenteamaniac
134
asked 8 hours ago
Greenteamaniac
134
asked 8 hours ago
Greenteamaniac
134
asked 8 hours ago
Greenteamaniac
134
asked 8 hours ago
Greenteamaniac
134
134
add a comment |
add a comment |
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