non-Bayesian Estimation Research Articles

A new extension of Burr-Hatke exponential distribution with engineering and biomedical applications

In this study, the Topp-Leone family of distribution approach was used to modify the Burr Hatke Exponential distribution to provide adequate fits for some engineering and health data which previous existing distributions in the family of Burr Hatke Exponential have failed to do. The new distribution improves the robustness of Burr Hatke Exponential distribution by making it capable of modeling emerging new world complex data with varying features, possesses greater capacity and flexibility to model lifetime data, has better goodness of fit. Some mathematical properties of the derived distribution such as quantile function, moments, order statistics, entropies, etc were obtained and discussed. Some non-Bayesian estimation approaches like maximum likelihood estimation (ML), maximum Product spacing estimation (MPSE), Least squares estimation (LS), weighted least squares estimation (WLS), Cramer-von-Mises estimation (CVM), Anderson-Darling estimation (AD), and right-tailed Anderson Darling estimation (RTAD), as well as Bayesian method under independent gamma priors were adopted to estimate the parameters of the model and the various methods proved efficient. From the simulation results, the bias and root mean squared error for the parameters are relatively small and the become smaller as the sample size becomes larger. This shows convenience and improved estimation accuracy. We further constructed a regression model using the proposed distribution. Extensive simulation studies were used to determine the efficiency of the method in both the estimation of its parameters and that of the regression model. The TL-BHE regression was fitted on censored CD4 count data of HIV/AIDs patients. The competitiveness, applicability, and usefulness of the model were demonstrated using datasets and the results validate the theoretical findings. The results indicate that the TL-BHE distribution achieved better results than the baseline distribution and other variants of the classical distributions.

Bayesian and Non-Bayesian Estimation for The Parameter of Inverted Topp-Leone Distribution Based on Progressive Type I Censoring

Bayesian and Non-Bayesian Estimation for The Parameter of Inverted Topp-Leone Distribution Based on Progressive Type I Censoring

Simulation Study for Estimating the Parameters and Reliability Function of Weighted Exponential Distribution with Fuzzy Data

This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information availableisin the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function linksequalimportance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently

Estimation of Stress - Strength Reliability for Parallel Redundant System Via Burr of type X Distribution

Estimation for the reliability of a parallel redundant system with independent stress and strength Burr distribution (type ) probability density functions is considered. Estimation of the reliability parameters is conducted according to the non-Bayesian estimation methods, namely the maximum likelihood and shrinkage methods. The Bayesian estimation is also considered using the Jeffery and Gamma priors with squared error, quadratic and weighted loss functions. Finally, the reliability estimate is calculated and the best method for estimation for each case is given using the mean squared error criteria.

Bayesian and Non-Bayesian Estimation for the Shape Parameters of New Versions of Bivariate Inverse Weibull Distribution based on Progressive Type II Censoring

Bayesian and Non-Bayesian Estimation for the Shape Parameters of New Versions of Bivariate Inverse Weibull Distribution based on Progressive Type II Censoring

Comparing some estimation methods for Frechet Distribution (Simulation)

The Frechet distribution, widely utilized in various fields such as hydrology, finance, and environmental sciences, poses challenges in parameter estimation, This study aims to compare several estimation methods for the Frechet distribution under scenarios with outlier observations. We consider both classical and robust estimation techniques, including ( Maximum Likelihood Estimation (MLE), Method of Moments (MOM), Least Squares Estimation (LSE), and Robust Regression methods(RRE)). To evaluate the performance of these methods, extensive simulation studies are conducted under different sample sizes and intial parameter values .mean squared error, are employed to assess the accuracy and robustness of each method under varying conditions. Our findings provide insights into the effectiveness and limitations of different estimation approaches for the Frechet distribution when simulation parameters are present, aiding practitioners in selecting suitable methods for robust parameter estimation in practical applications. Simulation results show that estimation method effected with (sample size, initial parameter values and evaluation criteria) , Bayesian estimation methods can be compared with Non-Bayesian estimation methods for Frechet distribution.

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets.

Simulation Study of the Bayesian and Non-Bayesian Estimation of a new Lifetime Distribution Parameters with Increasing Hazard Rate

In this paper, a new distribution known as the Shifted Chris-Jerry (SHCJ) distribution is proposed. The proposition is motivated by the need to compare the efficiency of various classical estimation methods as well as the bayesian estimation using gamma prior at linear-exponential loss, squared error loss and generalized entropy loss functions. Some useful mathematical properties are derived. Single acceptance sampling plans (SASPs) are created for the distribution when the life test is truncated at a predetermined period. The median lifetime of the SHCJ distribution with pre-defined constants is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the SHCJ distribution’s parameters, and the truncation time including numerical results are obtained. A simulation study is carried out for the bayesian and non-bayesian estimation of the parameters. Data on blood cancer patients is used to demonstrate the usefuleness of the proposed distribution.

Bayesian and non-Bayesian estimation of dynamic cumulative residual Tsallis entropy for moment exponential distribution under progressive censored type II

Abstract The dynamic cumulative residual (DCR) entropy is a helpful randomness metric that may be used in survival analysis. A challenging issue in statistics and machine learning is the estimation of entropy measures. This article uses progressive censored type II (PCT-II) samples to estimate the DCR Tsallis entropy (DCRTE) for the moment exponential distribution. The non-Bayesian and Bayesian approaches are the recommended estimating strategies. We obtain the DCRTE Bayesian estimator using the gamma and uniform priors via symmetric and asymmetric (linear exponential and general entropy) loss functions (LoFs). The Metropolis–Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distribution. The accuracy of different estimates for various sample sizes, is implemented via Monte Carlo simulations. Generally, we note based on the simulation study that, in the majority of cases, the DCRTE Bayesian estimates under general entropy followed by linear exponential LoFs are preferable to the others. The accuracy measure of DCRTE Bayesian estimates using a gamma prior has smaller values than the others using a uniform prior. As sample sizes grow, the Bayesian estimates of the DCRTE are closer to the true value. Finally, analysis of the leukemia data confirmed the proposed estimators.

Bayesian and non-Bayesian Estimation in log-logistic Lifetime model using Adaptive Progressively Censored Data

Bayesian and non-Bayesian Estimation in log-logistic Lifetime model using Adaptive Progressively Censored Data

Bayesian and Non-Bayesian Risk Analysis and Assessment under Left-Skewed Insurance Data and a Novel Compound Reciprocal Rayleigh Extension

Continuous probability distributions can handle and express different data within the modeling process. Continuous probability distributions can be used in the disclosure and evaluation of risks through a set of well-known basic risk indicators. In this work, a new compound continuous probability extension of the reciprocal Rayleigh distribution is introduced for data modeling and risk analysis. Some of its properties including are derived. The estimation of the parameters is carried out via different techniques. Bayesian estimations are computed under gamma and normal prior. The performance and assessment of all techniques are studied and assessed through Monte Carlo experiments of simulations and two real-life datasets for applications. Two applications to real datasets are provided for comparing the new model with other competitive models and to illustrate the importance of the proposed model via the maximum likelihood technique. Numerical analysis for expected value, variance, skewness, and kurtosis are given. Five key risk indicators are defined and analyzed under Bayesian and non-Bayesian estimation. An extensive analytical study that investigated the capacity to reveal actuarial hazards used a wide range of well-known models to examine actuarial disclosure models. Using actuarial data, actuarial hazards were evaluated and rated.

Analysis of information measures using generalized type-Ⅰ hybrid censored data

<abstract><p>An entropy measure of uncertainty has a complementary dual function called extropy. In the last six years, this measure of randomness has gotten a lot of attention. It cannot, however, be applied to systems that have survived for some time. As a result, the idea of residual extropy was created. To estimate the extropy and residual extropy, Bayesian and non-Bayesian estimators of unknown parameters of the exponentiated gamma distribution are generated. Bayesian estimators are regarded using balanced loss functions like the balanced squared error, balanced linear exponential and balanced general entropy. We use the Lindley method to get the extropy and residual extropy estimates for the exponentiated gamma distribution based on generalized type-Ⅰ hybrid censored data. To test the effectiveness of the proposed methodologies, a simulation experiment was carried out, and the actual data set was studied for illustrative purposes. In summary, the mean squared error values decrease as the number of failures increases, according to the results obtained. The Bayesian estimates of residual extropy under the balanced linear exponential loss function perform well compared to the other estimates. Alternatively, the Bayesian estimates of the extropy perform well under a balanced general entropy loss function in the majority of situations.</p></abstract>

The Double Burr Type XII Model: Censored and Uncensored Validation Using a New Nikulin-Rao-Robson Goodness-of-Fit Test with Bayesian and Non-Bayesian Estimation Methods

After studying the mathematical properties of the Double Burr XII model, we present Bayesian and non-Bayesian estimation for its unknown parameters. Also, we constructed a new statistical test for goodness-of-fit in case of complete and censored samples. The modified test is developed based on the Nikulin-Rao-Robson statistic for validation. Simulations are performed for assessing the new test along with nine applications on real data.

Non-Bayesian and Bayesian estimation of stress-strength reliability from Topp-Leone distribution under progressive first-failure censoring

ABSTRACT In this paper, the Bayesian and non-Bayesian estimation of based on the progressively first-failure censored data is considered. The and are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley’s approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes.

Bayesian and Non-Bayesian Estimation Methods for Simulating the Parameter of the Akshaya Distribution

Bayesian and Non-Bayesian Estimation Methods for Simulating the Parameter of the Akshaya Distribution

Inference for reliability in a multicomponent stress-strength model from generalized inverted exponential lifetime distribution under progressive first failure censoring

This article considers the non-Bayesian and Bayesian estimation procedures for multicomponent stress-strength reliability (MSSR) from generalized inverted exponential lifetime distributions using a progressively first failure censoring scheme. For the non-Bayesian estimation method of MSSR, the maximum likelihood estimation method is used, and for the Bayesian estimation method, the Metropolis-Hastings algorithm is taken into account. Also, the highest posterior density credible interval and the asymptotic confidence interval for MSSR in the case of Bayesian and non-Bayesian estimation methods, respectively, are obtained. A Monte Carlo numerical study is conducted to compare different types of estimates. For illustrative purposes, a real data analysis is carried out.

A Discrete Exponential Generalized-G Family of Distributions: Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data

This paper introduces a new flexible probability tool for modeling extreme and zero-inflated count data under different shapes of hazard rates. Many relevant mathematical and statistical properties are derived and analyzed. The new tool can be used to discuss several kinds of data, such as “asymmetric and left skewed”, “asymmetric and right skewed”, “symmetric”, “symmetric and bimodal”, “uniformed”, and “right skewed with a heavy tail”, among other useful shapes. The failure rate of the new class can vary and can take the forms of “increasing-constant”, “constant”, “monotonically dropping”, “bathtub”, “monotonically increasing”, or “J-shaped”. Eight classical estimation techniques—including Cramér–von Mises, ordinary least squares, L-moments, maximum likelihood, Kolmogorov, bootstrapping, and weighted least squares—are considered, described, and applied. Additionally, Bayesian estimation under the squared error loss function is also derived and discussed. Comprehensive comparison between approaches is performed for both simulated and real-life data. Finally, four real datasets are analyzed to prove the flexibility, applicability, and notability of the new class.

Bayesian and Non-Bayesian Estimation of Extended Exponential Distribution under Type-I Progressive Hybrid Censoring

Bayesian and Non-Bayesian Estimation of Extended Exponential Distribution under Type-I Progressive Hybrid Censoring

Fuzzy System Reliability Analysis for Kumaraswamy Distribution: Bayesian and Non-Bayesian Estimation with Simulation and an Application on Cancer Data Set

This paper proposes the fuzzy Bayesian (FB) estimation to get the best estimate of the unknown parameters of a two-parameter Kumaraswamy distribution from a frequentist point of view. These estimations of parameters are employed to estimate the fuzzy reliability function of the Kumaraswamy distribution and to select the best estimate of the parameters and fuzzy reliability function. To achieve this goal we investigate the efficiency of seven classical estimators and compare them with FB proposed estimation. Monte Carlo simulations and cancer data set applications are performed to compare the performances of the estimators for both small and large samples. Tierney and Kadane approximation is used to obtain FB estimates of traditional and fuzzy reliability for the Kumaraswamy distribution. The results showed that the fuzziness is better than the reality for all sample sizes and the fuzzy reliability at the estimates of the FB proposed estimated is better than other estimators, it gives the lowest Bias and root mean squared error.

On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications

In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.