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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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 ...
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223 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, ...
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732 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 ...
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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 ...
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667 views

Fisher information matrix in logistic regression

I am self-studying the basics of logistic regression. I came across this sentence: In logistic regression expected and observed information matrixes are equal I am aware that the information ...
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530 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' function in the survreg.predict function in r. I have read an excellent response by Tery Therneau, author of the survival ...
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33 views

What methods are there for estimating distributions based on histograms?

I recently worked on a consulting project where a client wanted to estimate gamma and weibull distributions based purely on histograms rather than raw-data. I have never worked with problems like that ...
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83 views

How are the Rayleigh Distribution and Weibull Distribution related?

I am trying to work out a physically intuitive way of understanding how the Weibull arises. Also according to the Wikipedia entry on the Weibull distribution, there is some how a relation to the ...
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102 views

Convergence rate of the maximum of Weibull random variables to a Gumbel distribution

Given a sequence of iid samples $X_1, \dots, X_n,$ where each $X_i$ comes from a Weibull distribution with shape parameter $k$ and scale parameter $\lambda$. Then it is a well-known result that the ...
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91 views

How can I compare parametric and semiparametric survival models?

On a given dataset, I am running a semiprametric Cox proportional hazards model, together with a series of parametric models (Weibul, gamma, lognormal, exponential, etc.). How can I know which is ...
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120 views

Confidence bounds for Weibull MTTF

I have three times-to-failure (TTFs) as 28, 40, 43. I fit a Weibull distribution on the data, and want to calculate a 95% confidence interval for the mean-time-to-failure (MTTF). Using ...
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56 views

Weibull regression sensitive to scaling of predictors?

I'm running a Weibull regression and decided to simulate data to assure myself that the model is able to recover the true parameters. ...
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727 views

Monte Carlo simulation for fitting distributions (Weibull and log-normal)

I am working on a computer project which needs statistical analysis and I am not much of a statistic person. I have a Bluetooth (BT) detector device which detects passing Bluetooth devices (i.e one ...
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Weibull Distribution v/s Beta Distribution

I've recently fallen in love with the Weibull Distribution and have gotten a reason to see if there's a mapping of this distribution to an interval (0,1). After plotting the Beta Distribution against ...
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154 views

Likelihood function for a Weibull model

I have an assignment for my course Microeconometrics. Currently I am stuck on the following question You are asked to help out with the statistics of a medical study. We are interested in the time ...
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992 views

Weibull distribution with the negative shape parameter

Just wondering why in the literature Weibull distribution is always defined for positive shapes, whereas the extension in the negative direction is possible and has many useful properties. Suppose $X ...
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Confidence intervals for extreme value distributions

I have wind data that i'm using to perform extreme value analysis (calculate return levels). I'm using R with packages 'evd', 'extRemes' and 'ismev'. I'm fitting GEV, Gumbel and Weibull distributions,...
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261 views

Accelerated Failure Time scale parameter excessively large when data is right censored

I am using an accelerated failure time model with the Weibull distribution to predict failure times. My failure times range from 1 - 365, with many (80%) data points that are right censored (no ...
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85 views

Posterior distribution for Weibull scale parameter with censored data

I am modeling a survival problem using a Weibull distribution with known shape parameter $k$ and unknown scale parameter $\theta$. The PDF and CDF are given by, \begin{align} f(t|k,\theta)=\frac{k}{\...
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Prove that bias of MLE for Weibull process

In the case of fixed observation interval $[0,T]$ of a Weibull process, I learned that the MLE of the shape parameter $\beta$ and MLE of the scale parameter $\alpha$ are as follow: $$\frac{1}{\hat{\...
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Generating Correlated Random Variables following Weibull Distribution

I am working on analyzing power generation from geographically distributed wind farms. I have wind speed data that have been collected at multiple locations, but the measurement periods for different ...
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152 views

Proof of alternative parameterization of Weibull Survival Model

In Parametric Survival Models by German Rodrıguez (hyperlink at bottom), it is stated the Exponential and Weibull models can be parameterized in a linear form (with time parameterized as $\log(T)$). ...
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How to prove the existence of upper truncated point?

Currently I am working on a data-set seems to have a Weibull distribution. Problem is that not sure if Weibull or Truncated-Weibull is better to use. Any methods or Hypothesis test there to prove if ...
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50 views

Independent variables in truncated Weibull distribution

I am relative new to statistics and currently working on a problem about crash rate analysis. It is appears to be a zero-inflated scenario, then I decide to use the hurdle model. The first part will ...
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224 views

R_How to select hyperprior distribution for Beta distribution parameter in R?

I have 2-mixture weibull distrubution. And this distribution haver the portion parameter θ whose value should lie between (0,1). Therefore, I am assuming the prior distribution of θθ to be a beta ...
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172 views

Detect the correct distribution from a small sample size by using fitdistrplus in R

The simplest version of the issue that I am looking for help is: How to detect the correct distribution from a small sample size in R by using fitdistrplus A simpler version: I am generating some ...
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184 views

Probability model for duration, how to write log-likelihood function for Weibull distribution to fit aggreate data

Background: I have a basic to moderate knowledge on probability and statistics. I have familiarity with R programming language and optimization routines. I'm reading an excellent article "Jobs, ...
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203 views

Why are these MLE estimates biased?

I estimate the parameters of survival data with censoring which is simulated from Weibull distribution. The mean time to event was set to 10 by choosing the combinations of shape and scale ...
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Variable effect in Weibull and Cox models

Is it possible to compare effect of variable on the survival time in the Cox model and in the Weibull regression model?
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Weibull distributed data for correlation analysis

On visual inspection of P-P plots, my time data appears to fit a Weibull distribution better than a normal distribution. I will use the variable for correlations and as a predictor in regression. In ...
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293 views

Spearman correlation of two Weibull distributions

Is there a way to find the Spearman correlation between two Weibull distributions? I need it as a parameter in a copula function for the joint Weibull distribution. I learned that using the Pearson ...
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33 views

Why did the log likelihood decrease with additional parameters?

I'm trying to decide the effect of some factors on the time for an event to happen . Specifically, I am looking at how long it takes for the subject to pass a test (recognize the stimulus) when ...
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48 views

Finding Quantiles and Sampling from a Mixture of Distributions

I am trying to replicate a result in this paper, specifically I am trying to implement the mixture distribution on page 9 of the document. The authors describe a hazard function: $$ h(x):=h_{1}(x) \...
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Hazard rate from Weibull vs. cumulative hazard plot does not match

) My problem is that I have HR for a factor named "Selvrisiko" and I get the output estimates (HR) (Upper bound) (Lower bound) as: but when I plot (Kaplan - Meier) cumulative hazard for the ...
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Testing for Constant Hazard Function

My colleagues and I have some unemployment data, and we'd like to test the hypothesis that it's drawn from a memoryless distribution (= constant hazard function). Is there a standard test for this? (...
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Weibull distribution fit

I have a random variable $X$ for which it is known a priori that $P(X > x) = \exp(-ax^b)$, i.e. the CDF is given by $F_X(x) = 1-\exp(-ax^b)$. I would like to determine the values of $a$ and $b$ ...
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Predicting survival probability at a future time for proportional hazard model

I have a Weibull proportional hazard model with fitted parameters $\lambda$ and $k$ and a time dependent covariate $x(t)$ with fitted coefficient $\beta$, such that the hazard function is given by, $...
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Using R to maximize a two parameter Weibull model via multivariate extension of Newton-Raphson method

I am just getting back into using R for the first time in a while, and wrote some code to perform the aforementioned task in the title. I was wondering if anyone could take a look at it and see if ...
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219 views

cumulative distribution function for non-normal distribution

From this article, I read that the author drew four versions of CDFs each plotted in different distributions (all four plots come from the same sample data) From these four plots, the author chooses ...
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186 views

R - nlm and Weibull Maximum Likelihood

Good day, I am working on an assignment where I have to Calculate the maximum likelihood estimates of $\alpha$ and $\lambda$ along with their standard erorrs on the basis of an independent and ...
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116 views

Moment generating function of a Weibull distribution and root finding heavy and light tailed case

I consider the equation $M_x(v)=1+(1+\beta)\mu$ and I need to find the solution $v>0$ such that the equation is fulfilled. For this example I consider the moment generating function $M_X(v)$ of a ...
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79 views

Estimation of a Weibull distribution. Overview of the methods

I'm looking for a method to estimate the parameters of a Weibull distribution from a given set of data. I know there are several method in literature, but I couldn't understand very well the ...
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55 views

Testing Parameter Restrictions in R

I've got duration data that I'm analyzing in R. The exponential and weibull distributions are both commonly used when constructing Accelerated Failure Time models for duration analysis/survival ...
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Has the Weibull distribution got pseudovariance?

I have a scholar question about the Weibull distribution, which can be parameterised, among other options, like follow: $f(t)= \lambda \alpha t^{\alpha-1}{exp} \left \{ \lambda t^\alpha \right \}$ ...
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48 views

Saddlepoint approximation with weibull distribution

I have some trouble with this computation, I have the moment generating function of a random variable $S$ by: $$M_S(t)=\frac{\beta\mu t}{1+(1+\beta)\mu t-M_X(t)}$$ According to the text that I am ...
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247 views

Survival distribution's parameter estimation in R with MLE

I have this life table, where: qx: the probability that someone aged exactly x will die before reaching age (x+1) dx: the number of people who die age x last birthday lx: the number of people who ...
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321 views

Algorithm for calculating beta and eta for weibull

I am writing code for drawing weibull plot in R. There are already some libraries for weibull and they are excellent. But they require ready beta and eta values for calculation of weibull function. In ...
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289 views

rearranging gamma functions to solve Weibull distribution parameters

I'm trying to generate a Weibull distribution to see if it fits some data. I have an arithmetic mean and variance for this data but I'm struggling to analytically create the specific Weibull ...
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1answer
64 views

Checking closeness of a mixture weibull and a mixture normal distribution to sample data

I have a sample data whose histogram shows a two peak distribution. So I generated two distributions which is the Mixture (average) of two (1) two weibull distributions (2) two normal distributions I ...
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51 views

Seeking advice on using time series estimation, for a specific type of data

I am new to time series modeling and am trying to come up with a solution for a problem. My problem is about estimation of next value in a time series, which is made of four components. One is picked ...