A time to failure distribution is said to have a Weibull distribution if the cumulative distribution function is given by F(t) 1 et , where , 0 Find the failure rate, and show that the Weibull distribution is IFR when 1 and DFR when 0 1 ...

which is nondecreasing if 1 non ...

A time-to-failure distribution is said to have a Weibull distribution if the cumulative distribution function is given

Question:

A time-to-failure is said to have a Weibull if the cumulative function is given by
F(t) = 1 –e–tβ /ƞ , where ƞ, β > 0.
Find the failure rate, and show that the Weibull is IFR when β ≥ 1 and DFR when 0 < β ≤ 1.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...