Questions tagged [weibull]

The Weibull distribution is a probability distribution with applications in survival analysis, reliability engineering, failure analysis, industrial engineering, extreme value theory, weather forecasting, forestry, and more.

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19
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1answer
25k views

Weibull distribution parameters $k$ and $c$ for wind speed data

Hi can the same be shown to obtain shape and scale parameter for modified maximum likelihood method
16
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1answer
13k views

Weibull Distribution v/s Gamma Distribution

What is the difference between the intuition behind Gamma and Weibull distributions? Is there any relationship between the two densities ? Kindly help.
5
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1answer
1k views

Expected survival time for Weibull proportional hazards model with R's predict.survreg

The predictions for a Weibull proportional hazards model from R's predict.survreg() are not the expected survival times. Please help me understand this behaviour. ...
4
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1answer
2k views

Analysis of variance with Weibull or Gamma distributions

I have been trying to find a method to analyse variance on Weibull and/or Gamma distributions but a Google search for anovar Weibull "gamma distribution" yields ...
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4answers
17k views

EM maximum likelihood estimation for Weibull distribution

Note: I am posting a question from a former student of mine unable to post on his own for technical reasons. Given an iid sample $x_1,\ldots,x_n$ from a Weibull distribution with pdf $$ f_k(x) = k x^{...
5
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1answer
2k views

How to find initial values for Weibull MLE in R?

I want to find parameter estimates using MLE for a weibull distribution to some data: 604 104 224 200 1444 1076 1308 6084 468 2308. My code is as follows: <...
6
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1answer
5k views

Mean survival time of a Weibull distribution

I'm trying to calculate the mean survival time of a Weibull distribution, and am getting what feels like an errant estimate of the mean--and each source I look up for how to calculate the mean gives a ...
7
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1answer
780 views

Comparing approaches of MLE estimates of a Weibull distribution

I need to parameterize a Weibull distribution to some data. Therefore, I use the Maximum-Likelihood-Estimation (MLE) from the fitdistrplus package in R. However, I wanted to understand what is done in ...
5
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1answer
3k views

Show that Weibull distribution can be transformed to exponential family

How do I show the Weibull distribution $f:(y; \lambda, \rho)$ can be transformed to the exponential family using the transformation $z=y^\lambda$? I know the form I need to express it in is $$\...
4
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1answer
5k views

Fitting Weibull distribution in R

My sample data: ...
4
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1answer
5k views

How can I recreate a Weibull distribution given mean and standard deviation and the shape and scale parameters are unknown?

Figure 2 is a Weibull distribution of three different wind farms in Canada. These 3 probability distributions were combined in a study to obtain a common wind speed model. I will be using this common ...
7
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1answer
2k views

Weibull vs. Gamma Distribution

I have data comprising distances between successive points on a line (1D vector): Traditionally in my field, such data is fitted with a gamma-distribution in an attempt to describe the distribution ...
3
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2answers
712 views

Is the multiple of a Weibull distributed variable also Weibull distributed?

A Weibull distributed variable $X \sim \textrm{Weibull}(\lambda, k)$ has probability density function $f(x):$ \begin{equation} f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left(\frac{x}{\...
2
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1answer
353 views

How to write this cost equation?

I have a mean time to failure variable that is Weibull-distributed with shape parameter less than $1$. Whenever a failure occurs, corrective action of cost $c_c$ is performed. From time to time, ...
1
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1answer
128 views

Generate Example data for which it is difficult to distinguish between Gamma, Weibull and log-normal fit using R?

I'm trying to generate a data set, as a demonstration case, to show a case in which it is difficult to distinguish between Gamma, Weibull and log-normal distribution. To do this I generate some data: ...
7
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3answers
3k views

Weibull Survival Model with Time Varying Covariates in R

I am trying to run a survival model using the Weibull approach, but the wrinkle is that I have time-varying covariates. I am using the survival package in R. My call is: ...
6
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3answers
1k views

Inconsistency between R and SAS for MLE on Weibull

I have the following data Y which I want to get an MLE estimate for the parameters using a Weibull distribution in R. 1468, 1872, 475, 1372, 3830, 1849, 978, ...
5
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1answer
1k views

Fitting a Weibull function in R

I am trying to model some data that follows a sigmoid curve relationship. In my field of work (psychophysics), a Weibull function is usually used to model such relationships, rather than probit. I am ...
4
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1answer
138 views

Standard Error of Ratio of Weibull variates

Assuming that I have 2 distinct random variables that follow a Weibull distribution, what's the standard error* of the ratio of these two random variables? Basically I have $X \sim \text{Weibull}, Y \...
4
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2answers
146 views

What do bootstrapped values of parameters tell you?

I tried to fit my data to the Weibull and I got the following output: I then used R to generate 10,000 bootstrapped parameters of fit values for a and I got this output (image2): Does this mean the ...
3
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1answer
3k views

Fit a Weibull distribution to…right-censored data?

Premise: I know next to nothing about survival analysis, I just started. I have a vector of failure times for some machines. Most of the machines (3362 vs 2694) are still running today, so I know they ...
2
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2answers
547 views

Parameter interpretation for discrete weibull regression

Please can someone provide an accessible interpretation of the parameter estimates from a discrete weibull regression model, e.g in R: ...
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1answer
311 views

Expectation of maximum of i.i.d Weibull random variables?

I'm trying to find an asymptotic approximation for the expectation of the maximum of $n$ Weibull random variables $X_i \sim Weibull(\lambda,\beta)$ when $\beta < 1/2$ and $n$ is large. From ...
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0answers
1k views

Predict probability of failure in R using survreg

I am fitting a weibull model as follows: s <- Surv(DFBR[,"Time"],DFBR[,"Censor"]) wei <- survreg(s~ Group+ UsefulLife, data = DFBR, dist="weibull") How ...