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.

Filter by
Sorted by
Tagged with
2
votes
1answer
409 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 ...
4
votes
1answer
346 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, ...
5
votes
0answers
668 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 ...
3
votes
2answers
712 views

How can I fit a weibull distribution based on the output of its pdf?

I have values which approximate the output of pdf(x) for a distribution over a range of x. I would like to determine the parameters of the two-parameter Weibull distribution which best fits these ...
6
votes
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 ...
3
votes
2answers
5k views

Is Weibull distribution a exponential family?

I'm wondering is Weibull distribution a exponential family?
0
votes
0answers
14 views

Problem of the pdf plot for Weibull distribution [duplicate]

I'm using MATLAB to plot the Weibull distribution function. But the y-axis, obviously, is not probability. Also, the plot on Wikipedia (here)has same y-axis as mine, so my question is: is there ...
1
vote
1answer
79 views

Is there any particular converging pattern for Least Square Estimators and Maximum Likelihood Estimators when we increasing the sample size?

My questions is: Is there any particular converging pattern for Least Square Estimators and Maximum Likelihood Estimators of Weibull distribution when we increase the sample size? is there any ...
3
votes
1answer
1k views

Estimating Weibull Distribution parameters by Least Square

I'm working on something about Least square estimation for Weibull distribution. After reviewing this paper, I'm pretty confused by the derivation of least square method. In this paper, the author ...
5
votes
1answer
355 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\...
1
vote
0answers
444 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 ...
3
votes
1answer
1k views

How can I estimate the goodness of fit of a nonlinear model in Python?

I have some data that I have fitted to a Weibull distribution and now I want to calculate the goodness of fit. At first I tried using the Kolmogorov-Smirnov test but I have read that this doesn't ...
2
votes
0answers
295 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 ...
1
vote
0answers
320 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 ...
1
vote
1answer
74 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 ...
6
votes
1answer
160 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. ...
3
votes
1answer
227 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 ...
0
votes
2answers
3k views

Meaning of Weibull scale and shape from flexsurvreg

I have used flexsurvreg to estimate the parameters of a Weibull distribution and got the following output. I would like to reconstruct the survival function to estimate the survival rate at a given ...
2
votes
0answers
260 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, ...
0
votes
1answer
453 views

Simulating survival times following a Weibull (or lognormal) distribution with ?% of right-censored observation [duplicate]

I'm trying to simulate survival times from Weibull(or lognormal) distribution with parameters (shape,scale) including (?%) of right-censored observations.I need to obtain observations of a variable, ...
1
vote
0answers
52 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 ...
-1
votes
1answer
926 views

Hazard Ratio Plot for Weibull Models

Can anyone help me out with plotting a Hazard Ratio Plot for a Weibull distribution. The following link specifies how a Hazard Ratio could be plotted for a Cox PH model: Plot of the estimated log ...
2
votes
0answers
3k views

When to use poisson distribution vs weibull distribution? [closed]

I have a simulator which simulates the jobs processed on different machines. I wish to model production of defective parts on the machines. So on a machine, I can model the time before the next defect ...
9
votes
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 ...
1
vote
1answer
381 views

correlation coefficient for non normal distribution (weibull)

I work with wind data. In order to estimate the strength of the correlation between two anenometers, in my department they usually calculate the pearson R. As far as I know the pearson R should be ...
1
vote
1answer
106 views

Why does the author subtract the minimum $\ln\,\ln([1-F(t)]^{-1}])$ for the Weibull plot?

When I read the Weibull Analysis Handbook (Abernethy et al., (1)), in Table 2.1 (p15), I don't really know how he gets the right-hand column ("Col 2 value - Min Col 2 value (-6,91)). Does he assume it ...
0
votes
1answer
400 views

What is the best way to handle two peak data?

Let's suppose, this is the histogram of flu patients data. As people gain flu more on autumn to winter, and more unlikely to gain flu on summer. Therefore, the amount of patients has different ...
1
vote
1answer
667 views

Probability Integral Transform: Standardising Data

I've been applying the probability integral transform as shown here: https://math.stackexchange.com/questions/592076/mapping-cdfs-to-each-other?noredirect=1&lq=1 I want to standardise the data ...
0
votes
1answer
611 views

Can I trust the result of AIC to test distribution

I'm trying to figure out which distribution is appropriate for my data. I use descdist() which is the package fitdistrplus in r. And here is my question. fit.weibull<-fitdist(dermat,"weibull&...
2
votes
0answers
377 views

It is possible to do a Multiple Weibull regression?

I have a response variable that I would like to explain with several predictors. The response variable is all positive continuous data. Some of the predictors are discrete while others are continuous. ...
1
vote
0answers
43 views

Survival analysis without a direct coupling between subjects and events

I am studying the failure rates of some components. The data that we possess are atypical for a survival analysis, however. The population and year of installation of components are known for the last ...
5
votes
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: <...
3
votes
0answers
846 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 ...
7
votes
1answer
1k 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 ...
1
vote
1answer
161 views

Survival analysis with large populations (upscaling sample to population)

Taking the data available from the survival() package, we can develop a survival curve and 95% CI, assuming an underlining weibull distibution. ...
3
votes
1answer
2k views

Meaning of flexsurv's flexsurvreg res.t outputs

I am trying to understand the meaning of the coefficients estimates of the output of flexsurv's flexsurvreg function. For example, let us assume I want to perform the survival analysis and fit of a ...
3
votes
2answers
1k 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}{\...
1
vote
0answers
185 views

Fitting Weibull PH model to Weibull mixture cure model

I generated a mixture cure model with Weibull distributed survival times (Weibull mixture cure model) . This is my baseline survival function conditional on the Bernoulli distributed covariate $X_i$ : ...
2
votes
1answer
633 views

Graphical verification of Weibull distribution

I want to verify whether Weibull is a good candidate for my distribution in survival analysis. So I plot log(t) vs log(-log(Kaplan-Meier). But instead of two lines, I get plot where the lines are ...
2
votes
2answers
794 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: ...
1
vote
0answers
256 views

Weibull, Gumbell and Extreme Value: from mean and variance to shape, scale and location parameter

I need to sample random numbers from Weibull, Gumbel and Generalized extreme value distributions. Of all of these distributions I know mean and variance. My question is: how can I determine these ...
0
votes
2answers
2k views

Can I fit a Weibull distribution on both positive and negative values (observations)?

I have dataset with observations having both positive and negative values. I would like to know if I can check if my dataset follows a Weibull distribution.
2
votes
0answers
815 views

Variance-Covariance matrix of Weibull Distribution for right-censored data

The probability distribution function, cumulative distribution function and survival function of Weibull distribution are given by respectively, \begin{equation} f(t;\alpha, \beta)= \dfrac{\beta}{\...
4
votes
0answers
1k views

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 ...
7
votes
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: ...
1
vote
0answers
147 views

Problem with initial guess in Newton-Raphson iteration method

I'm working on estimating the four parameters of Exponentiated Modified Weibull Extension Distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation (MLE). Because the ...
2
votes
0answers
47 views

Is there any way that this function can be a Weibull distribution?

I am currently working on a fatigue life analysis using an old airworthiness standard, Defence Standard 00-970, which was issued by the UK Minister of Defence for British designed military aircraft. ...
3
votes
0answers
162 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 ...
2
votes
1answer
168 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: ...
0
votes
1answer
1k views

UMVUE for $\theta$ in Weibull distribution

How can I find the UMVUE for $\theta$ in the following Weibull distribution? $$f\left(y|\theta\right) = \frac{2y}{\theta}\, \exp\left(-\frac{y^2}{\theta}\right),\: y>0, \theta>0$$ I want to ...