# Hazard Rate and Survivor Function

• rad0786
In summary, the hazard rate function is given by h(t) = lamda for 0 =< t =< 50 and h(t) = lamda + alpha(t - 50) for t > 50. The survivor function is S = e^-(lamda)t for 0 =< t =< 50. To find S'/S = -h, one would integrate ln(S) = -(Lt + At^2/2 - 50At + C), where L and A are constants, and D is a constant of integration.
rad0786
I really doubt that anybody would help me out on this...because by experience, nobody ever replies to the stats stuff on this forum...

But i'll try anyway

Question

the hazard rate function is:

h(t) = lamda > 0 ...... for 0 =< t =< 50

h(t) = lamda + alpha(t - 50) ... for t> 50

Find the surviovr function S'/S = -h.

Answer

So far...all i know is that S = e^-(lamda)t for 0 =< t =< 50

I'm not sure what to do from here...

Can somebody give me a boost please?

I would integrate. S'/S = ln(S)'

So calling lamda L and alpha A (I assume they're both constants, right?)
So ln(S) = -(Lt + At2/2 -50At + C) where C is a constant.

In fact, you missed for your other value of S that it's D*e-lamda*t because you didn't do what I did above, and missed the constant of integration

## 1. What is the hazard rate?

The hazard rate, also known as the failure rate, is a measure of the rate at which a certain event or failure occurs within a specific period of time. In the context of survival analysis, the hazard rate refers to the probability of an individual experiencing an event, such as death, at a given time interval.

## 2. How is the hazard rate related to the survivor function?

The survivor function, also known as the survival probability, is the probability that an individual will survive beyond a certain time point. The relationship between the hazard rate and survivor function is inverse; as the hazard rate increases, the survivor function decreases. This means that as an individual is more likely to experience the event, their probability of survival decreases.

## 3. Can the hazard rate change over time?

Yes, the hazard rate can change over time. In fact, it is common for the hazard rate to be non-constant in many real-world scenarios. For example, the hazard rate for a specific disease may be higher in the early stages of the disease and decrease over time as the patient receives treatment.

## 4. How is the hazard rate estimated?

The most commonly used method for estimating the hazard rate is the Kaplan-Meier estimator, which uses a non-parametric approach to estimate the survival function. This method takes into account the number of individuals who experience the event at a given time point, as well as the number of individuals who are still at risk of experiencing the event at that time point.

## 5. What is the difference between the hazard rate and the mortality rate?

The hazard rate and mortality rate are often used interchangeably, but they are not the same thing. The hazard rate measures the rate at which an event occurs, while the mortality rate measures the proportion of individuals who die within a specific time period. The hazard rate is a more general term that can be applied to any type of event, while the mortality rate specifically refers to death.

### Similar threads

• Calculus and Beyond Homework Help
Replies
4
Views
1K
• High Energy, Nuclear, Particle Physics
Replies
3
Views
968
• Calculus
Replies
18
Views
2K
• Calculus and Beyond Homework Help
Replies
10
Views
2K
• Calculus and Beyond Homework Help
Replies
15
Views
2K
• Calculus and Beyond Homework Help
Replies
1
Views
5K
• Differential Equations
Replies
2
Views
1K
• Mechanical Engineering
Replies
8
Views
3K
• Advanced Physics Homework Help
Replies
6
Views
2K
• Advanced Physics Homework Help
Replies
1
Views
2K