scholarly journals Statistical Inference for the Weibull Distribution Based on δ-Record Data

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Lina Maldonado ◽  
Gerardo Sanz
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Statistical Inference ◽  
Numerical Computation ◽  
Weibull Model ◽  
Rainfall Series ◽  
Estimation Of Parameters ◽  
Record Data

We consider the maximum likelihood and Bayesian estimation of parameters and prediction of future records of the Weibull distribution from δ -record data, which consists of records and near-records. We discuss existence, consistency and numerical computation of estimators and predictors. The performance of the proposed methodology is assessed by Montecarlo simulations and the analysis of monthly rainfall series. Our conclusion is that inferences for the Weibull model, based on δ -record data, clearly improve inferences based solely on records. This methodology can be recommended, more so as near-records can be collected along with records, keeping essentially the same experimental design.

Bayesian estimation of parameters of inverse Weibull distribution

2013 ◽  
Vol 40 (7) ◽  
pp. 1597-1607 ◽  
Author(s):  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Dinesh Kumar
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Estimation Of Parameters ◽  
Inverse Weibull Distribution

BAYESIAN ESTIMATION IN RANDOM CENSORSHIP MODEL FOR WEIBULL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250021 ◽  
Author(s):  
MUHAMMAD YAMEEN DANISH ◽  
MUHAMMAD ASLAM
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Real Data ◽  
Loss Functions ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Estimation Of Parameters ◽  
Random Censorship

This paper deals with Bayesian estimation of parameters in the proportional hazards model of random censorship for the Weibull distribution under different loss functions. We consider both the informative and noninformative priors on the model parameters to obtain the Bayes estimates using Gibbs sampling scheme. Maximum likelihood estimates are also obtained for comparison purposes. A simulation study is carried out to observe the behavior of the proposed estimators for different sample sizes and for different censoring parameters. One real data analysis is performed for illustration.

scholarly journals A New Exponential-X Family: Modeling Extreme Value Data in the Finance Sector

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
Rasool Roozegar ◽  
Morad Alizadeh ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Statistical Models ◽  
Claims Data ◽  
Maximum Likelihood Estimators ◽  
Weibull Model ◽  
Insurance Claims Data ◽  
Practical Analysis ◽  
Heavy Tailed ◽  
Modeling Data

In this paper, a family of statistical models, namely, a new exponential-X family is proposed. A subcase of the introduced family, called the new exponential-Weibull (NE-Weibull) model, is studied. The NE-Weibull model is very competent and possesses heavy-tailed properties. The maximum likelihood estimators of its parameters are derived. The consistency and efficiency of these estimators are assessed in a brief simulation study. Finally, the effectiveness of the NE-Weibull distribution is illustrated by modeling real insurance claims data. The practical analysis shows that the NE-Weibull distribution outclassed other distributions and it can be a better choice for modeling data in the finance sector.

scholarly journals AN APPLICATION OF THE POISSON-WEIBULL MODEL FOR CENSURED DATA

2021 ◽  
Vol 39 (4) ◽  
pp. 505-521
Author(s):  
Valdemiro Piedade VIGAS ◽  
Fábio PRATAVIERA ◽  
Giovana Oliveira SILVA
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Survival Data ◽  
Real Data ◽  
Weibull Model ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Kaplan Meier ◽  
Proposed Model ◽  
The Mean

In this paper, we proposed the Poisson-Weibull distribution for the modeling of survival data. The motivation to study this model since, in addition to generalizing the Weibull distribution, which is widely used in several areas of knowledge among them the Survival and Reliability analysis, it presents great exibility in the forms of the hazard function. The Poisson-Weibull distribution was created in a composition of discrete and continuous distributions where there is no information about which factor was responsible for the component failure, only the minimum lifetime value among all risks is observed. The maximum likelihood approach was used to estimate the parameters of the model. Also was conducted a simulation study to examine the mean, the bias, and the root of the mean square error of the maximum likelihood estimates of the proposed model according to the censoring percentages and sample sizes. The model selection criteria were also applied, in addition to graphic techniques such as TTT-Plot and Kaplan-Meier. Application to the real data set was used to illustrate the usefulnessof the distribution.

scholarly journals Maximum Likelihood Estimation of Parameters for Advanced Continuously Reinforced Concrete Pavement (CRCP) Punchout Calibration Model

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Liangliang Chen ◽  
Feng Zhang ◽  
Changjun Zhou
Keyword(s):  
Reinforced Concrete ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Concrete Pavement ◽  
Pavement Design ◽  
Regression Result ◽  
Calibration Model ◽  
Estimation Of Parameters

Pavement performance prediction is the essential part of the pavement design, which is very important for highway agencies for the purpose of budget allocating. This study introduces a model of local calibration for punchout, which is the major structural distress of continuously reinforced concrete pavement (CRCP). It is assumed that the number of equivalent single axle loads’ (ESALs) leads to punchout follows a Weibull distribution. The parameters of Weibull distribution were estimated by maximum likelihood estimation (MLE). Additionally, an approach of estimating the initial value of the parameters was also presented before applying the Newton method for solving the likelihood equations. The regression result was found to fit the performance-monitoring data from LTPP very well. The proposed calibration model is capable of describing the punchout and can be employed to predict the failure rate and reliability of CRCP in the pavement design and the arrangement of rehabilitation activities.

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