Questions tagged [weibull-distribution]

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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25
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4answers
20k 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^{...
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1answer
17k 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.
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1answer
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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
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2answers
8k views

What is the difference between a distribution and a process (Poisson)?

I'm doing my PhD in geomechanics. I thought we use a Poisson-Weibull distribution (for the variability of a parameter at the rock), but reading more about the subject I think maybe is a Poisson-...
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4answers
60k views

Can I use a Z-score with skewed and non-normal data? [closed]

I've been working with some process cycle time data and scaling using the standard z-score in order to compare between parts of the full cycle time. Should I use some other transformation since the ...
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1answer
2k views

Is there a multivariate version of the Weibull distribution?

I hope this one is self-explanatory, but let me know if something is unclear: Is there a multivariate version of the Weibull distribution?
10
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1answer
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Relationship between Gumbel and Weibull distribution, accelerated failure time models, and Survreg using R

I have three questions concerning accelerated failure time models (AFT), one statistical, one regarding how to implement these models in R, and one related to finding out information about what R is ...
9
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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 ...
8
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3answers
4k 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: ...
7
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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, ...
7
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2answers
206 views

Intuition behind Weibull distribution?

I don't understand the physical meaning of Weibull distribution's $k$ parameter. Here is a simplified formula of cumulative probability function of Weibull in the simplest form: $$p(\xi \geq x) = e^{-(...
7
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1answer
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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. ...
7
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1answer
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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 ...
7
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0answers
255 views

asymptotic unbiasedness of weibull mle

It's known that the MLEs of the two-parameter Weibull distribution scale and shape parameters are not available in a closed form. It is, however, known that they do exist, are unique, and moreover, ...
6
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1answer
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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 ...
6
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1answer
118 views

Marginal density of $X_1$ given that $X_1 + X_2 = d$ where $X_1$ and $X_2$ are iid Weibull?

In their tutorial (page 23) on heavy-tailed distributions, Nair et al. present the following graph (taken from a pre-publication chapter from a book by the same authors): Pictured are the marginal ...
6
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1answer
2k views

Compare two Weibull distributions

I want to compare two Weibull distributions fitted to two different datasets. Both datasets have a distribution that resembles the Weibull so the idea was to compare the fitted Weibull distributions ...
6
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1answer
166 views

$\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1)

I'm trying to find the expectation of log(max/min) from n samples of Weibull(alpha, 1). But I keep failing. Can anybody give some hints? I tried: $\mathbb{E}(\log(X_{max}/X_{min}) ) = \int_0^{\...
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2answers
4k views

Confidence intervals of fitted Weibull survival function?

I'm implementing a Weibull survival analysis fitter, and have successfully estimated the parameters and their standard errors. I can also produce the fitted survival curve. My question is how can I ...
6
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1answer
927 views

How would you visualize the difference between Cox/Weibull regression?

I'm trying to figure a way of properly displaying the difference\resemblance between various regression values on the same data set, using cox ph, weibull regression and log-normal regression. ...
6
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1answer
164 views

Probability one Weibull is less than another, given upper-bound

I have two random variables $X$ and $Y$, representing times-to-event, drawn from Weibull distributions. When $Y$ occurs, then $X$ cannot occur after that. Aside from this, we can assume independence. ...
6
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1answer
187 views

Weibull Mixture question

Is it possible that a mixture of Weibull RVs is also Weibull distributed, and if yes, what are the necessary conditions?
6
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1answer
153 views

distribution for scaled Maximum of n independent Weibulls for $n \to \infty$

Assume that $X_1, X_2,...\sim Weibull(\lambda, k) \quad iid.$, i.e. $F(X_1\leq x) = 1-e^{-(\lambda x)^k}$ define $M_n:= \max\{X_1, ..., X_n\}$ and $\tilde{M}_n:=\frac{M_n-b_n}{a_n}$ according to ...
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2answers
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How can I test the difference of two Weibull distributions?

I have two Weibull distribution sets from two wind datasets in order to check whether they are same. I thought a 2 sample t-test would be applicable but I couldn't find any ways to do that on the ...
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0answers
5k views

Conjugate of Weibull with shape known

This isn't exactly a homework problem but rather a self-selected problem I'm doing to prepare for a midterm. I can see from Wikipedia that it is an inverse gamma but I am unable to reach the ...
5
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4answers
1k views

Weibull distribution from given mean

I want to pull random numbers from a Weibull distribution. The formulas for this use scale and shape parameters (both of which I have), but not a mean parameter. How can I 'build' a Weibull ...
5
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1answer
12k views

Fitting Weibull distribution in R

My sample data: ...
5
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1answer
3k views

Right-censored survival fit with JAGS

Update: I got the JAGS model running and this eliminates the distracting part of my question. It's really about the proper preparation of data for dinterval() and inits. I can't find a concrete ...
5
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1answer
2k 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 ...
5
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1answer
1k views

Interpretation of Weibull Accelerated Failure Time Model Output

In this case study I have to assume a baseline Weibull distribution, and I'm fitting an Accelerated Failure Time model, which will be interpreted by me later on regarding both hazard ratio and ...
5
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1answer
360 views

Integrating out a gamma-distributed parameter from a Weibull distribution

I'm dealing with a variation of the three-parameter Weibull distribution where the third parameter is randomly distributed over a Gamma distribution. The cdf takes the form: $$ G(x|\gamma) = 1-\exp\...
5
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1answer
3k 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: <...
5
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1answer
996 views

Determine Weibull parameters (scale and shape) from hazard rate

I have a hazard rate given by a 2-parameters Weibull distribution, in the form: $$h(t) = \cfrac{B}{A} \, \left({\cfrac{t}{A}}\right)^{B - 1}$$ where $A=$ scale parameter and $B=$ shape parameter. I ...
5
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1answer
205 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 \...
5
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1answer
280 views

Adapt Kolmogorov-Smirnov Test to Lilliefors Test

I'm using EasyFit to fit distributions to a sample of data and test with the Kolmogorov-Smirnov test whether the null hypothesis may be rejected or not. But as this test estimates the parameters from ...
5
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1answer
139 views

Uniformly Most Powerful Test for Weibull Distribution

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: Let $Y_1,\dots,Y_n$ be a random sample from the probability density function given by $$f(y|\...
5
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1answer
4k 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 ...
5
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1answer
3k views

Why is the Weibull distribution considered as a model for lifetime of a system where parts are getting worn-out?

My question is: how one derives a Weibull distribution for a lifetime of a system where parts are wearing out with time? Provided that this is the lifetime analysis with aging is the main application ...
5
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1answer
4k 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 $$\...
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2answers
2k views

scipy.stats failing to fit Weibull distribution unless location parameter is constrained

Here is a demo set of data points that are drawn from a larger sample. I fit a Weibull distribution in R using the {fitdistrplus} package, and get back reasonable ...
5
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1answer
778 views

Predict Failure time/ Weibull analysis

Suppose I want to predict how many machine are going to fail in the next three years. The data collected are in days, so we want to predict no. of fails in next 1095 days. All the machines (100 of ...
5
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2answers
760 views

Tail distribution of sum of Weibull distributed variables

Is there a bound on the tail distribution of a finite sum of i.i.d Weibull random variables?
5
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2answers
687 views

Interpreting intercept of parametric AFT survival model (predict.survreg output)

I am trying to work out under what circumstances you would use the response type in the survreg.predict function in r. I have ...
4
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1answer
3k views

Identifying parameters for Weibull distribution from research paper

I am reading this paper: http://research.microsoft.com/en-us/um/people/ryenw/papers/LiuSIGIR2010.pdf I wish to use it to model web dwell time. I am not extremely well educated in the realm of stats....
4
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1answer
4k views

Why do coxph() and survreg(, dist="exponential") NOT return the same coefficient (except for expected opposite sign) in R?

If I understand correctly, the coefficient of a covariate X under a Weibull accelerated failure time (AFT) model is related to the ...
4
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1answer
355 views

How to generate random failure time conditional to a lower bound

For my Monte Carlo simulation (job related) I needed to generate random numbers with conditional probability of related distribution. (example: given that an item has been working for 1200 hours, ...
4
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1answer
125 views

Conditional mean of Weibull to the power of N

How can I (is it possible to) derive the conditional expectation of a variable $w$ that follows a 2 parameter Weibull Distribution $W(\lambda,k)$ with $\lambda$ scale parameter and $k$ shape parameter?...
4
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1answer
9k views

R - Weibull Distribution Parameters (Shape and Scale) - Confidence Intervals

I am wondering how you would obtain Scale and Shape parameter values on a Weibull Distribution's Confidence Interval bands (95% CI). The following post nicely illustrates confidence interval bands ...
4
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1answer
273 views

Reduce a Weibull model to an exponential one

I have this problem: Let $\ X\sim Weibull(\theta_1;\theta_2)$ with the sample: ...
4
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1answer
106 views

Probability of Weibull RV conditional on another Weibull RV

Let $X, Y$ be independent Weibull distributed random variables and $x>0$ a constant. Is there a closed form solution to calculating the probability $$P(X<x|X<Y)?$$ Or maybe a way to ...

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