How to find limit of hazard function

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Discussion Overview

The discussion revolves around finding the limit of a hazard function, specifically focusing on the integral of a function λ over a specified range as the upper limit approaches infinity. Participants explore the implications of different variables and functions involved in the limit process.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents the limit of the integral of λu as T approaches infinity, but the notation and definitions are unclear.
  • Another participant requests clarification on the variables T, t, and λ, indicating confusion over their definitions and roles in the limit.
  • A different participant introduces the concept of a hazard function represented as FR=λ(t), suggesting λ(t) is non-negative and questioning the limit of the integral as it approaches infinity.
  • One participant critiques the initial post for introducing terms like "FR" without prior context, leading to further confusion about the relationship between λ and the limits of integration.
  • Another participant calculates the limit of the integral under the assumption that λ is constant, concluding that the limit does not exist as T approaches infinity.
  • A later reply inquires whether T refers to the resolution of the hazard function, suggesting a potential interpretation of the variables involved.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the definitions and implications of the variables involved. There is no consensus on the correct interpretation or resolution of the limit problem.

Contextual Notes

Limitations include unclear definitions of T, t, and λ, as well as the dependence on the specific form of the function λ. The discussion does not resolve the mathematical steps necessary to clarify the limit process.

Who May Find This Useful

Readers interested in hazard functions, limits in calculus, or those preparing for tests involving these concepts may find the discussion relevant.

rawand
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lim(∫λu du)

when limit T tend to infinity and ∫ between 0 to t
 
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You need to clarify. T, t, λ.
 
FR=λ(t)
λ(t)>= 0
whay
lim∫λ(u)du→∞
not:lim(t → ∞)
∫ btween(0,t)

please i have test
thanks
 
That makes it even more non-understandable. At first you had [itex]\int \lambda u du[/itex] but then you say "[itex]FR= \lambda(t)[/itex]. You hadn't mentioned "FR" before and now it looks like [itex]\lambda[/itex] is a function of t (by which I guess you mean "T", the upper limit in the original integral.

What you first posted, [itex]\lim_{T\to\infty}\int_0^T \lambda u du[/itex] is fairly easy.
[tex]\lambda\int_0^T udu= \lambda T^2/2[/tex].
That limit, as T goes to infinity, does not exist. (Or the limit is "infinity" which just says it does not exist for a particular reason- it grows without bound.)

The second one you posted depends upon exactly what function of T [itex]\lambda[/itex] is.
 
Hey rawand and welcome to the forums.

Just out of curiosity, does T refer to the resolution of the hazard function? (Higher t means more values between 0 and t)
 

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