scholarly journals Stress-Strength Reliability for Exponentiated Inverted Weibull Distribution with Application on Breaking of Jute Fiber and Carbon Fibers

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Wael S. Abu El Azm ◽  
Ehab M. Almetwally ◽  
Abdulaziz S. Alghamdi ◽  
Hassan M. Aljohani ◽  
Abdisalam Hassan Muse ◽  
...  
Keyword(s):  
Real Life ◽  
Distance Estimation ◽  
Least Square ◽  
Likelihood Method ◽  
Interval Length ◽  
Unknown Parameters ◽  
Least Square Estimation ◽  
Monte Carlo Simulation Study ◽  
Von Mises ◽  
Percentile Bootstrap

For the first time and by using an entire sample, we discussed the estimation of the unknown parameters θ 1 , θ 2 , and β and the system of stress-strength reliability R = P Y < X for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when X and Y are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real‐life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

scholarly journals Comparison of Poisson and Quasi-Poisson Regression: A Simulation study

2021 ◽  
pp. 1-8
Author(s):  
A Gabriella ◽  
S Abdullah ◽  
S M Soemartojo
Keyword(s):  
Poisson Regression ◽  
Real Life ◽  
Least Square ◽  
Likelihood Method ◽  
Life Data ◽  
Real Life Data ◽  
Application Data ◽  
Newton Raphson ◽  
Simulation Results ◽  
Construction Parameter

Poisson regression is often used to model count data. However, it requires the assumption of equidispersion which not always met in the real application data. Quasi-Poisson can be considered as an alternative to handle this problem. The objective of this essay is to explain about the Quasi-Poisson regression, the likelihood construction, parameter estimation, and its implementation in real life data. The numerical method used in this study is Newton-Raphson which is equivalent to Iterative Weighted Least Square (IWLS) at the end of calculation. The simulation results for the data with the above problem showed that, in case of overdispersion, Quasi-Poisson regression with Maximum Quasi-Likelihood method provided a good fit to the data compared to Poisson regression.

scholarly journals Robustness Test of Selected Estimators of Linear Regression with Autocorrelated Error Term: A Monte-Carlo Simulation Study

2021 ◽  
pp. 1-17
Author(s):  
Rauf Ibrahim Rauf ◽  
Okoli Juliana Ifeyinwa ◽  
Haruna Umar Yahaya
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Linear Regression ◽  
Simulation Study ◽  
Explanatory Variable ◽  
Real Life ◽  
Least Square ◽  
Monte Carlo Simulation Study ◽  
Error Terms

Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.

scholarly journals A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020 ◽  
Vol 8 (2) ◽  
pp. 610-630 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Emrah Altun EA ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Survival Times ◽  
New Model ◽  
Von Mises ◽  
Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

The shifted Gompertz-G family of distributions: Properties and applications

2021 ◽  
Vol 71 (5) ◽  
pp. 1291-1308
Author(s):  
Joseph Thomas Eghwerido ◽  
Friday Ikechukwu Agu
Keyword(s):  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Real Life ◽  
Likelihood Method ◽  
Test Statistic ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Proposed Model ◽  
Left And Right ◽  
Mean Variance

Abstract This article proposes a class of generator for classical statistical distribution called the shifted Gompertz-G (SHIGO-G) distribution for generating new continuous distributions. Special models of the proposed model were examined together with some of its statistical properties in closed form which makes it tractable for censored data. Its major properties include heavy tail, approximately symmetric, left and right skewed with a combination of exponential and a reverted Gumbel distributions called the Gompertz. The bivariate SHIGO-G is introduced. The parameters estimate of the proposed model was obtained by maximum likelihood method. A Monte Carlo simulation study was employed to investigate the performance of the estimators of the proposed model mean, variance, bias and mean square error. A two real life illustration was used to examine the empirical goodness-of-fit of the test statistic of the proposed model. The results of the real life applications show that the SHIGO-G model provides a better fit for the data set used.

Huber Estimation for Uncertain Autoregressive Model

2021 ◽  
pp. 2150010
Author(s):  
Zhe Liu
Keyword(s):  
Autoregressive Model ◽  
Prediction Interval ◽  
Real Data ◽  
Least Square ◽  
Time Analysis ◽  
Unknown Parameters ◽  
Least Square Estimation ◽  
Uncertain Variables ◽  
Carbon Dioxide Concentrations ◽  
Future Value

Traditional time analysis deals with observations in chronological order assuming the observations are precise numbers under the framework of probability theory, whereas data are imprecisely collected in many cases. This paper characterizes the imprecisely observed data as uncertain variables and estimates the unknown parameters in the uncertain autoregressive model using Huber loss function, which is more flexible compared with other robust estimations for a pre-given [Formula: see text] that regulates the amount of robustness. Then prediction value and prediction interval of the future value are given. What is more, a method to choose [Formula: see text] by cross-validation is proposed. At last, numerical examples show our methods in detail and illustrate the robustness of Huber estimation by comparing it with the least square estimation. black Our methods are also applied to a set of real data with carbon dioxide concentrations.

scholarly journals Half-Logistic Xgamma Distribution: Properties and Estimation under Censored Samples

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Rashad Bantan ◽  
Amal S. Hassan ◽  
Mahmoud Elsehetry ◽  
B. M. Golam Kibria
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Real Data ◽  
Least Square ◽  
Likelihood Method ◽  
Mean Residual Life ◽  
Model Parameters ◽  
Censored Samples ◽  
Von Mises

This paper proposed a new probability distribution, namely, the half-logistic xgamma (HLXG) distribution. Various statistical properties, such as, moments, incomplete moments, mean residual life, and stochastic ordering of the proposed distribution, are discussed. Parameter estimation of the half-logistic xgamma distribution is approached by the maximum likelihood method based on complete and censored samples. Asymptotic confidence intervals of model parameters are provided. A simulation study is conducted to illustrate the theoretical results. Moreover, the model parameters of the HLXG distribution are estimated by using the maximum likelihood, least square, maximum product spacing, percentile, and Cramer–von Mises (CVM) methods. Superiority of the new model over some existing distributions is illustrated through three real data sets.

scholarly journals Comparison of Poisson and Quasi-Poisson Regression: A Simulation study

2021 ◽  
pp. 1-7
Author(s):  
A Gabriella ◽  
S Abdullah ◽  
S M Soemartojo
Keyword(s):  
Poisson Regression ◽  
Real Life ◽  
Least Square ◽  
Likelihood Method ◽  
Life Data ◽  
Real Life Data ◽  
Application Data ◽  
Newton Raphson ◽  
Simulation Results ◽  
Construction Parameter

Poisson regression is often used to model count data. However, it requires the assumption of equidispersion which not always met in the real application data. Quasi-Poisson can be considered as an alternative to handle this problem. The objective of this essay is to explain about the Quasi-Poisson regression, the likelihood construction, parameter estimation, and its implementation in real life data. The numerical method used in this study is Newton-Raphson which is equivalent to Iterative Weighted Least Square (IWLS) at the end of calculation. The simulation results for the data with the above problem showed that, in case of overdispersion, Quasi-Poisson regression with Maximum Quasi-Likelihood method provided a good fit to the data compared to Poisson regression.

scholarly journals Bayesian and Classical Estimation for the One Parameter Double Lindley Model

2020 ◽  
pp. 409-420 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Wahhab Mohammed ◽  
Haitham M. Yousof
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Weighted Least Squares Method ◽  
Von Mises ◽  
New Distribution

The main motivation of this paper is to show how the different frequentist estimators of the new distribution perform for different sample sizes and different parameter values and to raise a guideline in choosing the best estimation method for the new model. The unknown parameters of the new distribution are estimated using the maximum likelihood method, ordinary least squares method, weighted least squares method, Cramer-Von-Mises method and Bayesian method. The obtained estimators are compared using Markov Chain Monte Carlo simulations and we observed that Bayesian estimators are more efficient compared to other the estimators.

scholarly journals Comparisons of six different estimation methods for log-Kumaraswamy distribution

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1839-1847
Author(s):  
Caner Tanis ◽  
Bugra Saracoglu
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Monte Carlo Simulation Study ◽  
Kumaraswamy Distribution ◽  
Bayesian Least Squares ◽  
Von Mises

In this paper, it is considered the problem of estimation of unknown parameters of log-Kumaraswamy distribution via Monte-Carlo simulations. Firstly, it is described six different estimation methods such as maximum likelihood, approximate bayesian, least-squares, weighted least-squares, percentile, and Cramer-von-Mises. Then, it is performed a Monte-Carlo simulation study to evaluate the performances of these methods according to the biases and mean-squared errors of the estimators. Furthermore, two real data applications based on carbon fibers and the gauge lengths are presented to compare the fits of log-Kumaraswamy and other fitted statistical distributions.

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