scholarly journals Gompertz Fréchet Strength of a component between two stresses Reliability Estimation

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Sarah Adnan ◽  
Nada Sabah Karam
Keyword(s):  
Maximum Likelihood ◽  
Sampling Methods ◽  
Reliability Estimation ◽  
Least Square ◽  
Scale Parameters ◽  
Fréchet Distribution ◽  
Distribution Parameters ◽  
Component Strength ◽  
Frechet Distribution ◽  
Better Than

In this paper, the reliability of the stress-strength model is derived for probability P( <X< ) of a component strength X between two stresses ,  , when X and ,  are independent Gompertz Fréchet distribution with unknown and known shape parameters and common known scale parameters. Different methods used to estimate R and Gompertz Fréchet distribution parameters which are [Maximum Likelihood, Least square, Weighted Least square, Regression and Ranked set sampling methods], and the comparison between these estimations by simulation study based on mean square error criteria. The comparison confirms that the performance of the maximum likelihood estimator works better than the other estimators.

scholarly journals Gompertz Fréchet stress-strength Reliability Estimation

2021 ◽  
pp. 4892-4902
Author(s):  
Sarah A. Jabr ◽  
Nada S. Karam
Keyword(s):  
Maximum Likelihood ◽  
Reliability Estimation ◽  
Least Square ◽  
Shape Parameters ◽  
Likelihood Estimator ◽  
Fréchet Distribution ◽  
Distribution Parameters ◽  
Estimate Reliability ◽  
Frechet Distribution ◽  
Better Than

In this paper, the reliability of the stress-strength model is derived for probability P(Y<X) of a component having its strength X exposed to one independent stress Y, when X and Y are following Gompertz Fréchet distribution with unknown shape parameters and known parameters . Different methods were used to estimate reliability R and Gompertz Fréchet distribution parameters, which are maximum likelihood, least square, weighted least square, regression, and ranked set sampling. Also, a comparison of these estimators was made by a simulation study based on mean square error (MSE) criteria. The comparison confirms that the performance of the maximum likelihood estimator is better than that of the other estimators.

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

scholarly journals Effectivity of Modified Maximum Likelihood Estimators Using Selected Ranked Set Sampling Data

2016 ◽  
Vol 38 (2) ◽  
Author(s):  
Tamanna Islam ◽  
Molla Rahman Shaibur ◽  
S.S. Hossain
Keyword(s):  
Maximum Likelihood ◽  
Ranked Set Sampling ◽  
Simple Random Sample ◽  
Exponential Distributions ◽  
Underlying Distribution ◽  
Population Mean ◽  
Scale Parameters ◽  
Modified Maximum Likelihood ◽  
Two Parameter ◽  
Better Than

This paper describes the modified maximum likelihood estimator (MMLE) of location and scale parameters based on selected ranked set sampling (SRSS) for normal, uniform and two-parameter exponential distributions. For these distributions, the MMLE of location and scale parameters for SRSS data were compared with the estimators of location and scale parameters for simple random sample (SRS) and ranked set sample (RSS). The MMLE based on SRSS data were found to be advantageous as compared to SRS and RSS estimators for the same number of measurements. The SRSS method with errors in ranking was also described. The minimum correlation between the actual and erroneous ranking was required for MMLE of SRSS to achieve better precision than usual SRS and RSS estimators. When the wrong assumption about the underlying distribution was present, the MMLE of the population mean based on SRSS was better than the RSS estimator ofthe population mean for all the cases considered.

scholarly journals Beta Generalized Exponentiated Frechet Distribution with Applications

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 687-697
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Information Matrix ◽  
Model Parameters ◽  
Fréchet Distribution ◽  
Method Of Maximum Likelihood ◽  
Frechet Distribution ◽  
Fisher's Information

Abstract In this article we introduce a new six - parameters model called the Beta Generalized Exponentiated-Frechet (BGEF) distribution which exhibits decreasing hazard rate. Many models such as Beta Frechet (BF), Beta ExponentiatedFrechet (BEF), Generalized Exponentiated-Frechet (GEF), ExponentiatedFrechet (EF), Frechet (F) are sub models. Some of its properties including rth moment, reliability and hazard rate are investigated. The method of maximum likelihood isproposed to estimate the model parameters. The observed Fisher’s information matrix is given. Moreover, we give the advantage of the (BGEF) distribution by an application using two real datasets

scholarly journals MODELING AND COMPARISON OF MAXIMUM LIKELIHOOD AND MEDIAN RANK REGRESSION METHODS WITH FRÉCHET DISTRIBUTION

2020 ◽  
Vol 2 (2) ◽  
pp. 159-168
Author(s):  
Maryam Firdos ◽  
Kamran Abbas ◽  
Shahab Ahmed Abbasi ◽  
Nosheen Yousaf Abbasi
Keyword(s):  
Maximum Likelihood ◽  
Rank Regression ◽  
Regression Methods ◽  
Fréchet Distribution ◽  
Median Rank ◽  
Frechet Distribution

scholarly journals Estimating the Reliability Function of some Stress- Strength Models for the Generalized Inverted Kumaraswamy Distribution

2021 ◽  
pp. 240-251
Author(s):  
Hakeem Hussain Hamad ◽  
Nada Sabah Karam
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Least Square ◽  
Mean Square ◽  
Kumaraswamy Distribution ◽  
Scale Parameters ◽  
Strength Models ◽  
Best Estimator

This paper discusses reliability of the stress-strength model. The reliability functions 𝑅1 and 𝑅2 were obtained for a component which has an independent strength and is exposed to two and three stresses, respectively. We used the generalized inverted Kumaraswamy distribution GIKD with unknown shape parameter as well as known shape and scale parameters. The parameters were estimated from the stress- strength models, while the reliabilities 𝑅1, 𝑅2 were estimated by three methods, namely the Maximum Likelihood,  Least Square, and Regression.  A numerical simulation study a comparison between the three estimators by mean square error is performed. It is found that best estimator between the three estimators is Maximum likelihood estimators.  

Sign in / Sign up

Export Citation Format

Share Document