Name of a Particular Distribution Family
I am looking for the name and some reference of the following particular distribution family. Suppose the CDF is $F(x)$, then it has the following property:$$1-F(x;theta)=[1-F(x)]^theta.$$
Intuitively, F(x) is something like $1-(1-H(x))^theta$. Someone suggested that it is called proportional hazard distribution. But I hardly saw any reference on that. Is there any particular name of the family of probability distributions that satisfy this property?
probability statistics probability-distributions density-function
asked Oct 31 at 1:54
Terry
856
add a comment |
I am looking for the name and some reference of the following particular distribution family. Suppose the CDF is $F(x)$, then it has the following property:$$1-F(x;theta)=[1-F(x)]^theta.$$
Intuitively, F(x) is something like $1-(1-H(x))^theta$. Someone suggested that it is called proportional hazard distribution. But I hardly saw any reference on that. Is there any particular name of the family of probability distributions that satisfy this property?
probability statistics probability-distributions density-function
asked Oct 31 at 1:54
Terry
856
add a comment |
I am looking for the name and some reference of the following particular distribution family. Suppose the CDF is $F(x)$, then it has the following property:$$1-F(x;theta)=[1-F(x)]^theta.$$
Intuitively, F(x) is something like $1-(1-H(x))^theta$. Someone suggested that it is called proportional hazard distribution. But I hardly saw any reference on that. Is there any particular name of the family of probability distributions that satisfy this property?
probability statistics probability-distributions density-function
asked Oct 31 at 1:54
Terry
856
I am looking for the name and some reference of the following particular distribution family. Suppose the CDF is $F(x)$, then it has the following property:$$1-F(x;theta)=[1-F(x)]^theta.$$
Intuitively, F(x) is something like $1-(1-H(x))^theta$. Someone suggested that it is called proportional hazard distribution. But I hardly saw any reference on that. Is there any particular name of the family of probability distributions that satisfy this property?
probability statistics probability-distributions density-function
probability statistics probability-distributions density-function
asked Oct 31 at 1:54
Terry
856
asked Oct 31 at 1:54
Terry
856
asked Oct 31 at 1:54
Terry
856
asked Oct 31 at 1:54
Terry
856
asked Oct 31 at 1:54
Terry
856
856
add a comment |
add a comment |
1 Answer
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I think the exponential distribution will satisfy the requirement.
$F(x) = 1-e^{-x}$.
$1-F(x;theta) = 1-(1-e^{-theta x}) = e^{-theta x}$.
$[1-F(x)]^theta = [1-(1-e^{-x})]^theta = (e^{-x})^theta = e^{-theta x}$
answered Nov 23 at 5:44
Aditya Dua
80418
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
I think the exponential distribution will satisfy the requirement.
$F(x) = 1-e^{-x}$.
$1-F(x;theta) = 1-(1-e^{-theta x}) = e^{-theta x}$.
$[1-F(x)]^theta = [1-(1-e^{-x})]^theta = (e^{-x})^theta = e^{-theta x}$
answered Nov 23 at 5:44
Aditya Dua
80418
add a comment |
I think the exponential distribution will satisfy the requirement.
$F(x) = 1-e^{-x}$.
$1-F(x;theta) = 1-(1-e^{-theta x}) = e^{-theta x}$.
$[1-F(x)]^theta = [1-(1-e^{-x})]^theta = (e^{-x})^theta = e^{-theta x}$
answered Nov 23 at 5:44
Aditya Dua
80418
add a comment |
I think the exponential distribution will satisfy the requirement.
$F(x) = 1-e^{-x}$.
$1-F(x;theta) = 1-(1-e^{-theta x}) = e^{-theta x}$.
$[1-F(x)]^theta = [1-(1-e^{-x})]^theta = (e^{-x})^theta = e^{-theta x}$
answered Nov 23 at 5:44
Aditya Dua
80418
I think the exponential distribution will satisfy the requirement.
$F(x) = 1-e^{-x}$.
$1-F(x;theta) = 1-(1-e^{-theta x}) = e^{-theta x}$.
$[1-F(x)]^theta = [1-(1-e^{-x})]^theta = (e^{-x})^theta = e^{-theta x}$
answered Nov 23 at 5:44
Aditya Dua
80418
answered Nov 23 at 5:44
Aditya Dua
80418
answered Nov 23 at 5:44
Aditya Dua
80418
answered Nov 23 at 5:44
Aditya Dua
80418
80418
add a comment |
add a comment |
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