Talk:Weibull distribution

From Wikipedia, the free encyclopedia

I believe the graph needs replacing. the weibull reaches its max at t = a (b-1)^1/b / b^1/b, not at t=a.

Contents 1 Related distributions 2 Notation 3 Simplification of the mode 4 graphics with range of shape parameters would help article

[edit] Related distributions

Do I understand this correctly?: The exponential distribution and the Rayleigh distribution are contained in the definition of the Weibull distribution as special cases? If this is so, then I feel the article should state this more clearly (i.e. human-readable :-) ) --BjKa 14:58, 16 Jun 2005 (UTC)

The Weibull distribution is essentially an exponential distribution with an extra parameter 'k', that describes the time-dependance of the distribution. Remember that the exponential distribution describes a Poisson process: it describes the time T until a sample fails. The Weibull distribution also depicts the time T until a sample fails, but it doesn't require the sample failure chance to be independant of the time elapsed.

P(T < t₁ + t₂ | T > t1)! = P(T < t₂)

[edit] Notation

The notation here could use some work. The shape parameter is more commonly denoted at "beta" and the characteristic life (or scale parameter) as "eta" (sometimes "alpha"). I would fix it, but I don't know how to fix the graphics to match.

Can we get some consistency in the parameter usage? I see lamdas, gammas, betas, k, and mu all floating around out there. I have read that standard usage involves parameters alpha and beta, not lamda and k.

This has always annoyed me about statistical distributions; We are not all professional statisticians.

Please see Template talk:probability distribution for template standards. As far as article standards go - We have been trying to use subscript f_k(...) for discrete probability density, where k is the random variate, and ... are the parameters. F_k(...) represents the CMF. For continuous, f(x | ...) is the PDF and F(x | ...) is the CDF, with x being the continuous random variate. The parameters are named according to whatever is "common" usage. I don't think setting them all to alphas and betas would be helpful. Generally μ stands for the location parameter (usually the mean), σ for the scale parameter (usually std. dev.) These "standards" are by no means universal and 80% of the time it just needs to be fixed, other times the non-standard usage is so widespread that it would be inappropriate to change it. Maybe we should write this down somewhere. PAR 14:39, 11 July 2005 (UTC)

The plots of the Weibull function in this article are not correct. For example, the curve for lambda=1 and k=2 has a mode of ~0.7 at x=~1 whereas it should be 0.86 at x=1/sqrt(2)=0.707. Likewise for the other plots. [8 April 2006]

[edit] Simplification of the mode

I think the mode is simpler to calculate when written this way:

if k > 1

It is currently

if k > 1

This is the first time I have made a submission - so I don't know what the process is here.

[edit] graphics with range of shape parameters would help article

Shape of distribution can change a great deal (at least when viewed as pdf) as shape parameter goes to 1 and then below 1. Would be very helpful to get graphics that show that. Would also be neat to show graphics of hazard rate with range of parameters. —The preceding unsigned comment was added by AndrewRA (talk • contribs) 09:50, 13 December 2006 (UTC).