Chen Distribution Research Articles

Modified Generalized Chen Distribution, Estimation and Application using Econometrics Data

In this study, a variant of the generalized Chen (GC) distribution with parameters α, β, γ, δ, and λ, termed the Modified Generalized Chen (MGC) distribution, was introduced. The study evaluated several Chen distribution variants theoretically, focusing on the MGC distribution. Variants considered include the Generalized Chen (GC), Half-Cauchy Chen (HCC), New Extended Chen (NEC), and Exponentially Generalized Modified Chen (EGMC) distributions. The objectives of the study was to derive the probability density function (PDF) and cumulative density function (CDF) of the MGC distribution, determine its statistical properties and reliability characteristics, compare these properties and characteristics to existing distributions, and empirically evaluate its performance. The study developed unique expressions for the PDF, CDF, survival function, and hazard function of the MGC distribution. By evaluating PDFs and performance measures such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and mean square error (MSE) across various datasets, the MGC distribution consistently demonstrated superiority over other variants. The MGC distribution offers improved model fit, predictive accuracy, and interpretability without sacrificing simplicity. The dataset employed in this study was the secondary data, encompassing economic indicators from 1981 to 2021 and public health expenditure data for Nigeria and Ghana from 1995 to 2014. Statistical analyses revealed that on the average, the MGC distribution outperforms others, with superior average AIC (-509.95), BIC (-510.49), and MSE (499.89) measures across the datasets considered in the study. This superior performance indicates better fit and accuracy in predicting economic and public health outcomes, offering valuable insights for policymakers and researchers. The study underscores the importance of adopting flexible and interpretable distribution models like the MGC distribution to enhance empirical analyses, inform policy decisions, and advance knowledge in econometrics and related disciplines.

Stress–strength reliability estimation of s-out-of-k multicomponent systems based on copula function for dependent strength elements under progressively censored sample

The main objective of this research is to determine the reliability of multicomponent stress–strength under progressive Type II censoring. The model comprises k independent strength components, and each component has two elements that are statistically dependent and exposed to the same random stress. To assess the correlation between their elements, we are utilizing the Gumbel copula and assuming that its parameter is unknown. The system is deemed operational only if at least certain number of strength variables s ( 1 ≤ s ≤ k ) surpass the random stress. We are using the Chen distribution to model the stress and strength variables, with varying shape parameters. Different methods are employed to estimate the unknown parameters, including maximum likelihood, maximum product of spacings, Cramér–von-Mises, and bootstrap confidence intervals. The effectiveness of these estimation techniques is evaluated through Monte Carlo simulation, and a real data set is analyzed to illustrate our procedures.

Bayesian and E-Bayesian Estimation for a Modified Topp Leone–Chen Distribution Based on a Progressive Type-II Censoring Scheme

Bayesian and E-Bayesian Estimation for a Modified Topp Leone–Chen Distribution Based on a Progressive Type-II Censoring Scheme

The Assessment of the Overall Lifetime Performance Index of Chen Products with Multiple Components

Process capability indices are widely utilized to evaluate process performance and drive continuous improvements in quality and productivity. Among these indices, the the-larger-the-better lifetime performance index is particularly noteworthy. For products with multiple components, an overall lifetime performance index is used, since it is a monotonically increasing function of the overall conforming rate and the relationship with each individual lifetime performance index can be determined. For products with the lifetime of the ith component following the Chen distribution, we investigate the maximum likelihood estimator for the overall lifetime performance index and the individual lifetime performance index based on the progressive type I interval censoring sample. Their asymptotic distributions for all lifetime performance indices are also derived. Once the target level for the overall lifetime performance index is specified, the desired level of individual lifetime performance index can be specified. By using the maximum likelihood estimator as the test statistic, a testing procedure to test whether the overall lifetime performance index has reached the target level is developed. The power analysis of the testing procedure is shown with figures, and some findings are summarized. At last, we use one practical example with two components to demonstrate how to implement this testing algorithmic procedure to test if the overall production process has reached the pre-assigned target level.

Estimation of the constant-stress model with bathtub-shaped failure rates under progressive type-I interval censoring scheme

This paper investigates constant-stress accelerated life tests interrupted by a progressive type-I interval censoring regime. We provide a model based on the Chen distribution with a constant shape parameter and a log-linear connection between the scale parameter and stress loading. Inferential methods, whether classical or Bayesian, are employed to address model parameters and reliability attributes. Classical methods involve the estimation of model parameters through maximum likelihood and midpoint techniques. Bayesian approximations are achieved via the utilization of the Metropolis–Hastings algorithm, Tierney-Kadane procedure, and importance sampling methods. Furthermore, we engage in a discourse on the estimation of confidence intervals, making references to both asymptotic confidence intervals and credible intervals. To conclude, we furnish a simulation study, a corresponding discussion, and supplement these with an analysis of real data.

Parameter estimation of Chen distribution under improved adaptive type-II progressive censoring

ABSTRACT This study focuses on the estimation of the two unknown parameters of Chen distribution, characterized by a bathtub-shaped hazard rate function, within an improved adaptive type-II progressive censored data framework. Maximum likelihood estimation is proposed for the two parameters, and the establishment of approximate confidence intervals is based on asymptotic normality. Bayesian estimation is also conducted under both symmetric and asymmetric loss functions, utilizing the proposed importance sampling and Metropolis–Hastings algorithm. Lastly, the performance of various estimation methods is evaluated through Monte Carlo simulation experiments, and the proposed estimation approach is illustrated using a real dataset.

FITTING G-FAMILY PROBABILITY DISTRIBUTION AT THE RAINFALL DATA OF RAJSHAHI DISTRICT, BANGLADESH

Classical statistical distributions were recognized tool in case of different areas such as biological science, economics, finance, engineering and environmental science. But these types of distribution have some limitations for modeling real data. Researchers are trying to find out the best performing statistical distribution for modeling environmental data by adding extra parameters in these existing distributions which provide super flexibility in modeling. These extend to new families of these distributions generally defined as G-family distribution. Rainfall is one of the most important natural resources for agricultural production. The excess and deficit amount of rainfall sometimes be dangerous for agriculture production. So, the prior knowledge about the pattern of rainfall will help to solve food insecurity, water erosion and water pollution problems. In this study we compare the performance of Gamma uniform G, Log gamma G type-I, Log gamma G type-II , Marshall-Olkin G and Weibull G distribution where we consider lomax, f, chen and Weibull distribution as baseline distribution for modeling the rainfall data in case of Rajshahi district Bangladesh. The monthly rainfall data from January 1971 to December 2020 consider as study period. The empirical study shows that Marshall-Olkin Chen distribution gives better fitting results in case of Rajshahi district. This study will help policy makers to become aware of upcoming situations for solving water related problems.

Inference of stress-strength reliability based on adaptive progressive type-Ⅱ censing from Chen distribution with application to carbon fiber data

<abstract><p>In this paper, we used the maximum likelihood estimation (MLE) and the Bayes methods to perform estimation procedures for the reliability of stress-strength $ R = P(Y < X) $ based on independent adaptive progressive censored samples that were taken from the Chen distribution. An approximate confidence interval of $ R $ was constructed using a variety of classical techniques, such as the normal approximation of the MLE, the normal approximation of the log-transformed MLE, and the percentile bootstrap (Boot-p) procedure. Additionally, the asymptotic distribution theory and delta approach were used to generate the approximate confidence interval. Further, the Bayesian estimation of $ R $ was obtained based on the balanced loss function, which came in two versions here, the symmetric balanced squared error (BSE) loss function and the asymmetric balanced linear exponential (BLINEX) loss function. When estimating $ R $ using the Bayesian approach, all the unknown parameters of the Chen distribution were assumed to be independently distributed and to have informative gamma priors. Additionally, a mixture of Gibbs sampling algorithm and Metropolis-Hastings algorithm was used to compute the Bayes estimate of $ R $ and the associated highest posterior density credible interval. In the end, simulation research was used to assess the general overall performance of the proposed estimators and a real dataset was provided to exemplify the theoretical results.</p></abstract>

New extension for Chen distribution based on [0, 1] Truncated Nadarajah-Haghighi-G family with two real data application

New extension for Chen distribution based on [0, 1] Truncated Nadarajah-Haghighi-G family with two real data application

Exponentiated Inverse Chen distribution: Properties and applications

A new distribution having three parameters called Exponentiated Inverse Chen distribution is proposed in this study. Important statistical properties like Survival function, hazard rate function, skewness and kurtosis etc are studied. Some methods of estimation Least Square, Maximum likelihood and Cramer-Von Mises methods are used using R programming software. A data set is discussed and Validity of the model is tested by analyzing P-P and Q-Q plots. Different information criteria such as Akanke’s information criterion, Bayesian information criterion, Corrected Akanke’s information criterion, and Hannan – Quinn information criterion are applied for model comparisons. For testing the goodness of fit of the proposed model, Kolmogrov-Smirnov, Anderson darling and Cramer –Von Mises statistics are used. The proposed model called Exponentiated Inverse Chen distribution is more applicable as compared to some existing probability model. It is found that MLEs are better with respect to LSE and CVM. PDF curve of model has shown that it can have various shapes like increasing as well as decreasing, monotonically increasing, constant as well as inverted bathtub shaped based hazard function is seen. Applicability and suitability of model is evaluated. For this, we have considered a real-life dataset. We found distribution that EIC is much flexible.

Parameters Estimation of the Exponentiated Chen Distribution Based on Upper Record Values

This article discusses the Bayesian and frequentist inferences for the exponentiated Chen distribution assuming upper record values. Due to unavailability of the compact form of marginal posterior distributions, a Markov Chain Monte Carlo algorithm is designed to compute the posterior summaries. Prediction of future record values under Bayesian and frequentist methods is also discussed mathematically and numerically. Further, a sensitivity analysis to assess the effect of prior on the estimated parameters is also a part of this study. Besides the simulation studies, the importance of the present study is illustrated with the help of a real data example. It is noted that the Bayes estimates outperform the frequentist inference.

On a Mixture of Bivariate Chen Distribution

On a Mixture of Bivariate Chen Distribution

Exponentially Generated Modified Chen Distribution with Applications to Lifetime Dataset

In this paper, the exponentially generated system was used to modify a two-parameter Chen distribution to a four-parameter distribution with better performance. The property of complete probability distribution function was used to verify the completeness of the resulting distribution, which shows that the distribution is a proper probability distribution function. A simulation study involving varying sample sizes was used to ascertain the asymptotic property of the new distribution. Small and large sample sizes were considered which shows the closeness of the estimates to the true value as the sample size increases. Lifetime dataset were used for model comparison which shows the superiority of exponentially generated modify Chen distribution over some existing distributions. It is therefore recommended to use the four-parameter Chen distribution in place of the well-known two-parameter Chen distribution.

Employ Stress-Strength Reliability Technique in Case the Inverse Chen Distribution

This paper uses classical and shrinkage estimators to estimate the system reliability (R) in the stress-strength model when the stress and strength follow the Inverse Chen distribution (ICD). The comparisons of the proposed estimators have been presented using a simulation that depends on the mean squared error (MSE) criteria.

Different estimation techniques for constant-partially accelerated life tests of chen distribution using complete data

The issue of various estimation techniques in constant partially accelerated life tests with complete data is the main subject of this research. The Chen distribution is regarded as an item’s lifetime under use conditions. To estimate the distribution parameters and the acceleration factor, maximum likelihood estimation, least square estimation, weighted least square estimation, Cramér Von–Mises estimation, Anderson–Darling estimation, right-tail Anderson–Darling estimation, percentile estimation, and maximum product of spacing estimation are presented for classical estimation. For illustrative purposes, two real data sets are analyzed. The investigation of the two real data sets reveals that the suggested techniques are practical and can be used to solve some engineering-related issues. In order to compare the results of the several estimation techniques that have been offered based on mean square error and absolute average bias, a simulation study is presented at the end. When adopting the smallest values for mean square error and absolute average bias, this study demonstrates that maximum product of spacing estimation is the technique that is most effective among the alternatives in most cases.

The Chen Autoregressive Moving Average Model for Modeling Asymmetric Positive Continuous Time Series

In this paper, we introduce a new dynamic model for time series based on the Chen distribution, which is useful for modeling asymmetric, positive, continuous, and time-dependent data. The proposed Chen autoregressive moving average (CHARMA) model combines the flexibility of the Chen distribution with the use of covariates and lagged terms to model the conditional median response. We introduce the CHARMA structure and discuss conditional maximum likelihood estimation, hypothesis testing inference along with the estimator asymptotic properties of the estimator, diagnostic analysis, and forecasting. In particular, we provide closed-form expressions for the conditional score vector and the conditional information matrix. We conduct a Monte Carlo experiment to evaluate the introduced theory in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications in a wind-speed and maximum-temperature time-series dataset.

The Chen–Perks Distribution: Properties and Reliability Applications

In this paper, a statistical distribution is presented that possesses the ability to describe failure rates exhibiting both monotonic and non-monotonic behaviors, and the bathtub curve, which represents the performance of a device in reliability engineering. The proposed distribution is based on the sum of the hazard functions of the Chen distribution and the Perks distribution, thus presenting the Chen–Perks distribution (CPD). Statistical properties of the CPD focused on reliability engineering are presented to make the model attractive to practitioners of the discipline. The parameters of the CPD were calculated via the maximum likelihood estimator. On the other hand, a comparative analysis was conducted in three study cases to determine the behavior of the CPD relative to other distributions that can describe failure times with the shape of a bathtub curve. The results show that the CPD can offer competitive results, which practitioners can consider when conducting reliability analysis.

Half-Cauchy Chen Distribution with Theories and Applications

In this article, we have suggested the three-parameter half-Cauchy Chen distribution which has been derived by compounding a continuous Chen distribution with the half-Cauchy family of distribution. The hazard rate function (HRF), quantile function, reversed hazard rate function, survival function, cumulative distribution function (CDF), probability density function (PDF), kurtosis, and skewness of the suggested distribution are some of its statistical properties and characteristics that are explored. Utilizing the methods of LSE, CVM, and MLE, the parameters of the new distribution are computed. All the calculations are performed with the aid of R programming software. To assess the application of the new distribution, two real data sets are analyzed and performed the goodness-of-fit. It is found that the half-Cauchy Chen distribution outperformed a few other existing distributions. We hope that this distribution will contribute to the field of real data analysis.

A New Right-Skewed One-Parameter Distribution with Mathematical Characterizations, Distributional Validation, and Actuarial Risk Analysis, with Applications

Skewed probability distributions are important when modeling skewed data sets because they provide a way to describe the shape of the distribution and estimate the likelihood of extreme events. Asymmetric probability distributions have the potential to handle and assess problems in actuarial risk assessment and analysis. To that end, we present a new right-skewed one-parameter distribution. In this work and for this purpose, a right-skewed probability distribution was derived and analyzed. The new distribution outperformed the exponential distribution, the Pareto distribution, the Chen distribution, and others in the field of actuarial risk analysis. Some useful key risk indicators are considered and analyzed to analyze the risks and for comparison with the competitive model. Several actuarial risk functions and indicators are evaluated and analyzed using the U.K. insurance claims data set. The process of risk assessment and analysis was carried out using a comprehensive simulation. For the purposes of distributional validity, a modified chi-squared type test is presented and employed in the testing process. The new, modified chi-squared type test that is used is simply an extension of the Rao–Robson–Nikulin test. In this work, the distributional validity is presented and analyzed under right-skewed censored and uncensored data sets.

The Discrete Exponentiated-Chen Model and Its Applications

A novel discrete exponentiated Chen (DEC) distribution, which is a subset of the continuous exponentiated Chen distribution, is proposed. The offered model is more adaptable to analyzing a wide range of data than traditional and recently published models. Several important statistical and reliability characteristics of the DEC model are introduced. In the presence of Type-II censored data, the maximum likelihood and asymptotic confidence interval estimators of the model parameters are acquired. Two various bootstrapping estimators of the DEC parameters are also obtained. To examine the efficacy of the adopted methods, several simulations are implemented. To further clarify the offered model in the life scenario, the two applications, based on the number of vehicle fatalities in South Carolina in 2012 and the final exam marks in 2004 at the Indian Institute of Technology at Kanpur, are analyzed. The analysis findings showed that the DEC model is the most effective model for fitting the supplied data sets compared to eleven well-known models in literature, including: Poisson, geometric, negative binomial, discrete-Weibull, discrete Burr Type XII, discrete generalized exponential, discrete-gamma, discrete Burr Hatke, discrete Nadarajah-Haghighi, discrete modified-Weibull, and exponentiated discrete-Weibull models. Ultimately, the new model is recommended to be applied in many fields of real practice.