Non-monotone hazard functions
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I should start with the caveat that I am relatively new to Survival analysis. I was watching a Hulu documentary about Crocodiles last night, and they mentioned that baby crocodiles have a low chance of survival when they are young, but "with each passing day they have fewer predators". It seems that this should be true for most (if not all animals) including Humans (maybe to a lesser extent).
It seems that this early stage of life could be modeled with a monotonically decreasing hazard function such as this one from a $Gamma(1/2, 1)$ distribution. 
Of course if we want to know the hazard function for the duration of the Crocodiles life, the Hazard function should eventually increase due to old age. All of the common parametric models that I have looked at (weibull, pareto, gamma, etc) are monotone, with the exception of Lognormal which is concave down.
Are there any simple parametric distributions which have a concave up (bowl shaped) Hazard function?
survival parametric hazard demography
edited 2 hours ago
kjetil b halvorsen
29.5k980216
asked 5 hours ago
knrumseyknrumsey
1,401315
$endgroup$
add a comment |
$begingroup$
I should start with the caveat that I am relatively new to Survival analysis. I was watching a Hulu documentary about Crocodiles last night, and they mentioned that baby crocodiles have a low chance of survival when they are young, but "with each passing day they have fewer predators". It seems that this should be true for most (if not all animals) including Humans (maybe to a lesser extent).
It seems that this early stage of life could be modeled with a monotonically decreasing hazard function such as this one from a $Gamma(1/2, 1)$ distribution.
Of course if we want to know the hazard function for the duration of the Crocodiles life, the Hazard function should eventually increase due to old age. All of the common parametric models that I have looked at (weibull, pareto, gamma, etc) are monotone, with the exception of Lognormal which is concave down.
Are there any simple parametric distributions which have a concave up (bowl shaped) Hazard function?
survival parametric hazard demography
edited 2 hours ago
kjetil b halvorsen
29.5k980216
asked 5 hours ago
knrumseyknrumsey
1,401315
$endgroup$
1
$begingroup$
That could be called a U-formed hazard function. See books.google.no/…
$endgroup$
– kjetil b halvorsen
3 hours ago
$begingroup$
@kjetilbhalvorsen Yep that looks right. Do you know of any parametric distributions with this type of Hazard function?
$endgroup$
– knrumsey
3 hours ago
$begingroup$
Its also known as a bathtube function! See Wikipedia and references there. Specifically Gompertz-Makeham. Many more hits on google, one is researchgate.net/publication/…
$endgroup$
– kjetil b halvorsen
2 hours ago
$begingroup$
@kjetilbhalvorsen That's what I'm looking for! If you want to quickly add this as an answer I will accept it. Thanks!
$endgroup$
– knrumsey
2 hours ago
add a comment |
$begingroup$
I should start with the caveat that I am relatively new to Survival analysis. I was watching a Hulu documentary about Crocodiles last night, and they mentioned that baby crocodiles have a low chance of survival when they are young, but "with each passing day they have fewer predators". It seems that this should be true for most (if not all animals) including Humans (maybe to a lesser extent).
It seems that this early stage of life could be modeled with a monotonically decreasing hazard function such as this one from a $Gamma(1/2, 1)$ distribution.
Of course if we want to know the hazard function for the duration of the Crocodiles life, the Hazard function should eventually increase due to old age. All of the common parametric models that I have looked at (weibull, pareto, gamma, etc) are monotone, with the exception of Lognormal which is concave down.
Are there any simple parametric distributions which have a concave up (bowl shaped) Hazard function?
survival parametric hazard demography
edited 2 hours ago
kjetil b halvorsen
29.5k980216
asked 5 hours ago
knrumseyknrumsey
1,401315
$endgroup$
I should start with the caveat that I am relatively new to Survival analysis. I was watching a Hulu documentary about Crocodiles last night, and they mentioned that baby crocodiles have a low chance of survival when they are young, but "with each passing day they have fewer predators". It seems that this should be true for most (if not all animals) including Humans (maybe to a lesser extent).
It seems that this early stage of life could be modeled with a monotonically decreasing hazard function such as this one from a $Gamma(1/2, 1)$ distribution.
Of course if we want to know the hazard function for the duration of the Crocodiles life, the Hazard function should eventually increase due to old age. All of the common parametric models that I have looked at (weibull, pareto, gamma, etc) are monotone, with the exception of Lognormal which is concave down.
Are there any simple parametric distributions which have a concave up (bowl shaped) Hazard function?
survival parametric hazard demography
survival parametric hazard demography
edited 2 hours ago
kjetil b halvorsen
29.5k980216
asked 5 hours ago
knrumseyknrumsey
1,401315
edited 2 hours ago
kjetil b halvorsen
29.5k980216
asked 5 hours ago
knrumseyknrumsey
1,401315
edited 2 hours ago
kjetil b halvorsen
29.5k980216
edited 2 hours ago
kjetil b halvorsen
29.5k980216
edited 2 hours ago
kjetil b halvorsen
29.5k980216
29.5k980216
asked 5 hours ago
knrumseyknrumsey
1,401315
asked 5 hours ago
knrumseyknrumsey
1,401315
asked 5 hours ago
knrumseyknrumsey
1,401315
1,401315
1
$begingroup$
That could be called a U-formed hazard function. See books.google.no/…
$endgroup$
– kjetil b halvorsen
3 hours ago
$begingroup$
@kjetilbhalvorsen Yep that looks right. Do you know of any parametric distributions with this type of Hazard function?
$endgroup$
– knrumsey
3 hours ago
$begingroup$
Its also known as a bathtube function! See Wikipedia and references there. Specifically Gompertz-Makeham. Many more hits on google, one is researchgate.net/publication/…
$endgroup$
– kjetil b halvorsen
2 hours ago
$begingroup$
@kjetilbhalvorsen That's what I'm looking for! If you want to quickly add this as an answer I will accept it. Thanks!
$endgroup$
– knrumsey
2 hours ago
add a comment |
1
$begingroup$
That could be called a U-formed hazard function. See books.google.no/…
$endgroup$
– kjetil b halvorsen
3 hours ago
$begingroup$
@kjetilbhalvorsen Yep that looks right. Do you know of any parametric distributions with this type of Hazard function?
$endgroup$
– knrumsey
3 hours ago
$begingroup$
Its also known as a bathtube function! See Wikipedia and references there. Specifically Gompertz-Makeham. Many more hits on google, one is researchgate.net/publication/…
$endgroup$
– kjetil b halvorsen
2 hours ago
$begingroup$
@kjetilbhalvorsen That's what I'm looking for! If you want to quickly add this as an answer I will accept it. Thanks!
$endgroup$
– knrumsey
2 hours ago
1
1
$begingroup$
That could be called a U-formed hazard function. See books.google.no/…
$endgroup$
– kjetil b halvorsen
3 hours ago
$begingroup$
That could be called a U-formed hazard function. See books.google.no/…
$endgroup$
– kjetil b halvorsen
3 hours ago
$begingroup$
@kjetilbhalvorsen Yep that looks right. Do you know of any parametric distributions with this type of Hazard function?
$endgroup$
– knrumsey
3 hours ago
$begingroup$
@kjetilbhalvorsen Yep that looks right. Do you know of any parametric distributions with this type of Hazard function?
$endgroup$
– knrumsey
3 hours ago
$begingroup$
Its also known as a bathtube function! See Wikipedia and references there. Specifically Gompertz-Makeham. Many more hits on google, one is researchgate.net/publication/…
$endgroup$
– kjetil b halvorsen
2 hours ago
$begingroup$
Its also known as a bathtube function! See Wikipedia and references there. Specifically Gompertz-Makeham. Many more hits on google, one is researchgate.net/publication/…
$endgroup$
– kjetil b halvorsen
2 hours ago
$begingroup$
@kjetilbhalvorsen That's what I'm looking for! If you want to quickly add this as an answer I will accept it. Thanks!
$endgroup$
– knrumsey
2 hours ago
$begingroup$
@kjetilbhalvorsen That's what I'm looking for! If you want to quickly add this as an answer I will accept it. Thanks!
$endgroup$
– knrumsey
2 hours ago
add a comment |
1 Answer
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oldest
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$begingroup$
What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard function of humans, high but falling hazard first few years of life, a minimum around 9-10 years of life, then slowly increasing.
Googling with those terms will lead to much information. Much of interest here
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
$endgroup$
add a comment |
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$begingroup$
What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard function of humans, high but falling hazard first few years of life, a minimum around 9-10 years of life, then slowly increasing.
Googling with those terms will lead to much information. Much of interest here
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
$endgroup$
add a comment |
$begingroup$
What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard function of humans, high but falling hazard first few years of life, a minimum around 9-10 years of life, then slowly increasing.
Googling with those terms will lead to much information. Much of interest here
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
$endgroup$
add a comment |
$begingroup$
What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard function of humans, high but falling hazard first few years of life, a minimum around 9-10 years of life, then slowly increasing.
Googling with those terms will lead to much information. Much of interest here
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
$endgroup$
What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard function of humans, high but falling hazard first few years of life, a minimum around 9-10 years of life, then slowly increasing.
Googling with those terms will lead to much information. Much of interest here
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
answered 2 hours ago
kjetil b halvorsenkjetil b halvorsen
29.5k980216
29.5k980216
add a comment |
add a comment |
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1
$begingroup$
That could be called a U-formed hazard function. See books.google.no/…
$endgroup$
– kjetil b halvorsen
3 hours ago
$begingroup$
@kjetilbhalvorsen Yep that looks right. Do you know of any parametric distributions with this type of Hazard function?
$endgroup$
– knrumsey
3 hours ago
$begingroup$
Its also known as a bathtube function! See Wikipedia and references there. Specifically Gompertz-Makeham. Many more hits on google, one is researchgate.net/publication/…
$endgroup$
– kjetil b halvorsen
2 hours ago
$begingroup$
@kjetilbhalvorsen That's what I'm looking for! If you want to quickly add this as an answer I will accept it. Thanks!
$endgroup$
– knrumsey
2 hours ago