scholarly journals Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Alessandro Barbiero
Keyword(s):  
Monte Carlo Simulation ◽  
Weibull Distribution ◽  
Real Data ◽  
Discrete Distributions ◽  
Software Implementation ◽  
Discrete Models ◽  
Monte Carlo Simulation Study ◽  
Type Iii ◽  
Failure Data ◽  
Better Than

The type III discrete Weibull distribution can be used in reliability analysis for modeling failure data such as the number of shocks, cycles, or runs a component or a structure can overcome before failing. This paper describes three methods for estimating its parameters: two customary techniques and a technique particularly suitable for discrete distributions, which, in contrast to the two other techniques, provides analytical estimates, whose derivation is detailed here. The techniques’ peculiarities and practical limits are outlined. A Monte Carlo simulation study has been performed to assess the statistical performance of these methods for different parameter combinations and sample sizes and then give some indication for their mindful use. Two applications of real data are provided with the aim of showing how the type III discrete Weibull distribution can fit real data, even better than other popular discrete models, and how the inferential procedures work. A software implementation of the model is also provided.

scholarly journals The Gamma Generalized Pareto Distribution with Applications in Survival Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro
Keyword(s):  
Monte Carlo Simulation ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Generalized Pareto ◽  
Mathematical Properties ◽  
Pareto Model

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.

scholarly journals Parametric inference of Akash distribution for Type-Ⅱ censoring with analyzing of relief times of patients

2021 ◽  
Vol 6 (10) ◽  
pp. 10789-10801
Author(s):  
Tahani A. Abushal ◽  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Unknown Parameter ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Posterior Density ◽  
Monte Carlo Simulation Study ◽  
Reliability Characteristics ◽  
Highest Posterior Density

<abstract><p>In this paper, the problem of estimating the parameter of Akash distribution applied when the lifetime of the product follow Type-Ⅱ censoring. The maximum likelihood estimators (MLE) are studied for estimating the unknown parameter and reliability characteristics. Approximate confidence interval for the parameter is derived under the s-normal approach to the asymptotic distribution of MLE. The Bayesian inference procedures have been developed under the usual error loss function through Lindley's technique and Metropolis-Hastings algorithm. The highest posterior density interval is developed by using Metropolis-Hastings algorithm. Finally, the performances of the different methods have been compared through a Monte Carlo simulation study. The application to set of real data is also analyzed using proposed methods.</p></abstract>

scholarly journals Reliability Analysis of Structural Ceramic Components Using a Three-Parameter Weibull Distribution

1992 ◽  
Author(s):  
Stephen F. Duffy ◽  
Lynn M. Powers ◽  
Alois Starlinger
Keyword(s):  
Monte Carlo Simulation ◽  
Silicon Nitride ◽  
Weibull Distribution ◽  
Reliability Analysis ◽  
Simulation Methods ◽  
Structural Ceramic ◽  
Failure Data ◽  
Regression Estimators ◽  
Ceramic Components ◽  
Sintered Silicon

This paper describes nonlinear regression estimators for the three-parameter Weibull distribution. Issues relating to the bias and invariant associated with these estimators arc examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.

scholarly journals A Mixture of Two Burr Type III Distributions: Identifiability and Estimation under Type II Censoring

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
A. S. Al-Moisheer
Keyword(s):  
Monte Carlo Simulation ◽  
Real Data ◽  
Reliability Function ◽  
Type Ii ◽  
Estimation Technique ◽  
Numerical Illustration ◽  
Data Set ◽  
Type Ii Censoring ◽  
Type Iii ◽  
Statistical Library

The mixture of two Burr Type III distributions (MTBIIID) is investigated. First, the identifiability property of the MTBIIID is proved. Then, two different methods of estimation are used. Next, the estimates of the unknown five parameters and reliability function of the MTBIIID under Type II censoring are obtained. To study the performance of the estimation technique in the paper, a Monte Carlo simulation is presented. In addition, the numerical illustration requires solving nonlinear equations; therefore, the software international mathematical statistical library (IMSL) is used to assess these effects numerically. Finally, a real data set is applied to illustrate the methods proposed here.

scholarly journals A family of Gamma-generated distributions: Statistical properties and applications

2021 ◽  
pp. 096228022110092
Author(s):  
Hormatollah Pourreza ◽  
Ezzatallah Baloui Jamkhaneh ◽  
Einolah Deiri
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Hazard Functions ◽  
Distribution Probability ◽  
Method Of Maximum Likelihood ◽  
Special Case

In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15

scholarly journals Reliability Analysis of Structural Ceramic Components Using a Three-Parameter Weibull Distribution

1993 ◽  
Vol 115 (1) ◽  
pp. 109-116 ◽  
Author(s):  
S. F. Duffy ◽  
L. M. Powers ◽  
A. Starlinger
Keyword(s):  
Monte Carlo Simulation ◽  
Silicon Nitride ◽  
Weibull Distribution ◽  
Reliability Analysis ◽  
Simulation Methods ◽  
Structural Ceramic ◽  
Failure Data ◽  
Regression Estimators ◽  
Ceramic Components ◽  
Sintered Silicon

This paper describes nonlinear regression estimators for the three-parameter Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.

scholarly journals THE BETA-WEIBULL DISTRIBUTION ON THE LATTICE OF INTEGERS

2016 ◽  
Vol 39 (1) ◽  
pp. 40 ◽  
Author(s):  
Vahid Nekoukhou ◽  
Hamid Bidram ◽  
Rasool Roozegar
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Discrete Analog ◽  
Discrete Distributions ◽  
Hazard Rate Function ◽  
Data Set ◽  
Beta Weibull Distribution ◽  
New Distribution

In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contains several discrete distributions as special sub-models. Some distributional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined.

scholarly journals Inducing a desired value of correlation between two point-scale variables: a two-step procedure using copulas

2021 ◽  
Author(s):  
Alessandro Barbiero
Keyword(s):  
Computational Cost ◽  
Likelihood Estimation ◽  
Real Data ◽  
Discrete Distributions ◽  
Point Scale ◽  
Numerical Illustration ◽  
Monte Carlo Simulation Study ◽  
Marginal Distributions ◽  
Copula Parameter ◽  
Two Step Estimation

AbstractFocusing on point-scale random variables, i.e. variables whose support consists of the first m positive integers, we discuss how to build a joint distribution with pre-specified marginal distributions and Pearson’s correlation $$\rho $$ ρ . After recalling how the desired value $$\rho $$ ρ is not free to vary between $$-1$$ - 1 and $$+1$$ + 1 , but generally ranges a narrower interval, whose bounds depend on the two marginal distributions, we devise a procedure that first identifies a class of joint distributions, based on a parametric family of copulas, having the desired margins, and then adjusts the copula parameter in order to match the desired correlation. The proposed methodology addresses a need which often arises when assessing the performance and robustness of some new statistical technique, i.e. trying to build a huge number of replicates of a given dataset, which satisfy—on average—some of its features (for example, the empirical marginal distributions and the pairwise linear correlations). The proposal shows several advantages, such as—among others—allowing for dependence structures other than the Gaussian and being able to accommodate the copula parameter up to an assigned level of precision for $$\rho $$ ρ with a very small computational cost. Based on this procedure, we also suggest a two-step estimation technique for copula-based bivariate discrete distributions, which can be used as an alternative to full and two-step maximum likelihood estimation. Numerical illustration and empirical evidence are provided through some examples and a Monte Carlo simulation study, involving the CUB distribution and three different copulas; an application to real data is also discussed.

PARAMETER ESTIMATE WITH ONLY ONE COMPLETE FAILURE OBSERVATION USING MONTE CARLO EM ALGORITHM

2001 ◽  
Vol 08 (02) ◽  
pp. 109-122 ◽  
Author(s):  
WAN-KAI PANG ◽  
PING-KEI LEUNG ◽  
XIAO-LONG PU ◽  
SHI-SONG MAO
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Reliability Model ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Failure Data ◽  
Mcem Algorithm ◽  
Monte Carlo Em

In reliability studies, often we only have one failure data recorded in a life testing experiment. If there are two parameters in the reliability model, such as the model using Weibull distribution, then maximum likelihood estimation of parameters becomes a difficult problem. Mao and Chen published a real data set of the lifetime of a certain type of bearings which only contains one failure data. They used a Bayesian method to analyze the data and obtained some results for model parameter estimation. However, in their method the choice of prior distribution will affect heavily the final results. In this paper, we propose a Monte Carlo EM (MCEM) algorithm to estimate reliability model parameters using the Weibull distribution. Based on the same data set of Mao and Chen, we obtain some results using the MCEM algorithm. Our results do not depend on the choice of arbitrary prior distributions.

Parameter Estimations of Inverse Weibull Distribution

2011 ◽  
Vol 199-200 ◽  
pp. 564-568
Author(s):  
Wei An Yan ◽  
Bao Wei Song ◽  
Zhao Yong Mao ◽  
Huang Yong Le
Keyword(s):  
Monte Carlo Simulation ◽  
Weibull Distribution ◽  
Empirical Bayes ◽  
Bayes Estimation ◽  
Conjugate Prior ◽  
Monte Carlo Simulation Study ◽  
Empirical Bayes Estimation ◽  
Asymptotically Optimal ◽  
Parameter Estimations ◽  
Inverse Weibull Distribution

under entropy loss function, the E-Bayes estimation and empirical bayes estimation to the parameter of inverse Weibull distribution used conjugate prior are discussed. And we prove the empirical bayes estimation is asymptotically optimal. At last, the MSE of the estimations are compared based on Monte Carlo simulation study. According to these comparisons, it is suggested that the accuracy of E-Bayes estimation is close to the empirical bayes estimation.

Sign in / Sign up

Export Citation Format

Share Document