Lower Record Values Research Articles

Advancements in reliability estimation for the exponentiated Pareto distribution: a comparison of classical and Bayesian methods with lower record values

Advancements in reliability estimation for the exponentiated Pareto distribution: a comparison of classical and Bayesian methods with lower record values

Bayesian and empirical-Bayesian evaluations of the Topp–Leone lifetime model using lower record statistics

Record statistics are generally used to measure a process’ stochastic behavior at previously unheard-of values, either upper or lower. It can be obtained or calculated using order statistics from a sample whose size is dictated by the values and order of occurrence of observations. Due to its finite support and bathtub-shaped hazard function, the Topp–Leone (TL) distribution is appealing for reliability investigations. In today’s practical applications, estimating unknown parameters and predicting upcoming records is an essential issue. Thus, in this work, the TL distribution’s lower record values are taken into account. Against the symmetric squared-error loss, both Bayes and empirical-Bayes approaches are used to estimate the TL’s parameter and calculate prediction limits for upcoming lower record values. A Monte Carlo simulation experiment is performed to assess the accuracy of the estimation methodologies provided. To demonstrate the operability and usefulness of the various approaches, two useful applications are studied. The numerical evaluations show that the suggested approaches perform effectively and that the provided estimations are adequate in practice.

Reliability of stress–strength model for exponentiated Teissier distribution based on lower record values

Reliability of stress–strength model for exponentiated Teissier distribution based on lower record values

Statistical inference based on lower record values for the inverse Weibull distribution under the modified loss function

The main objective of this article is to develop a linear, exponential loss function (LXLF) to the dependability value and variables of the Inverse Weibull Distribution (IWD) according to Lowest Record Values. By weighting the LXLF to construct current function loss, the modified linear, exponential loss function (WLXLF) was named. Then use WLXLF to estimate the parameters and reliability functions of the (IWD). After that, we evaluated how well the prediction made in this article performed against the Bayesian estimator using the symmetric and asymmetric loss functions and maximum likelihood estimation (MLE). The credibility range for the values of the parameters and durability function has been created using the parametric bootstrap approach, and the outcomes have been contrasted via a Monte Carlo simulation. An actual data set from a realistic situation was utilized to explain the concept. The computer simulation results demonstrated that the suggested method, performed as expected, was the best for estimating the scale parameter and reliability function. The proposed technique performed well in estimating the shape parameter based on real data and had an acceptable performance for estimating scale parameters and reliability functions.

Characterizations of Topp–Leone Lomax Distribution based on the Generalized Lower Record Values

Characterizations of Topp–Leone Lomax Distribution based on the Generalized Lower Record Values

Some mathematical properties of Odd Kappa-G family

We present in this paper further mathematical properties of the Odd Kappa-G family of distributions. These structural properties of this family hold for any baseline model including characterizations results based on two truncated moments and hazard and reversed hazard functions. In addition, kth lower record values and extreme values of this Odd Kappa-G family are introduced. Lastly, the bivariate probability distributions of the Odd Kapp-G (BFGMOKG) family based on FGM copula are obtained.

Some Results on Exponentiated Weibull Distribution via Dual Generalized Order Statistics

In this paper, we use the concept of dual generalized order statistics dgos which was given by Pawlas and Syznal (2001). By using this, we obtain the various theorems and some relations through ratio and inverse moment by using exponentiated-Weibull distribution. Cases for order statistics and lower record values are also considered. Further, we characterize the exponentiated-Weibull distribution through three different methods by using the results obtained in this paper.

Interval Estimation of the Stress-Strength Reliability for Lower Record Data Based on One-parameter Exponential Distribution Using Median Ranked Set Sampling and Record Ranked Set Sampling

This paper develops interval estimation of stress-strength reliability when data are lower record values from a one-parameter exponential distribution using resampling schemes such as median ranked set sampling (MRSS) and record ranked set sampling (RRSS). For illustrative aims, we inspect the performance of the proposed interval estimation methods, bootstrap, and generalized confidence intervals (CIs) by using a simulation study and real examples. The result indicates that the proposed interval based on a bootstrap percentile (BP) CI and a generalized CI (GC) using MRSS is suitable for the application.

Some stochastic comparisons of lower records and lower record spacings

We obtain here sufficient conditions for increasing concave order and location independent more riskier order of lower record values based on stochastic comparisons of minimum order statistics. We further discuss stochastic orderings of lower record spacings. In particular, we show that increasing convex order of adjacent spacings between minimum order statistics is a sufficient condition for increasing convex order of adjacent spacings of their lower records.

On the record values and its predictions from Exponentiated Inverted Weibull distribution and associated inference

This paper deals with the lowest record values from the Exponentiated Inverted Weibull distribution. We establish exact expression for moments of lower record values and also derive the recurrence relations for single and product moments of the same. Then we estimate the location and scale parameters as well as obtain confidence intervals for location and scale parameters from location-scale Exponentiated Inverted Weibull distribution. We also worked on future lower record values. We discuss linear predictor and prediction interval for the future record values. Finally, with the help of real rainfall data, we presented all the methods discussed here.

Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution

This paper considers interval estimation of stress–strength reliability of k-out-of-n system when the stress and strength components follow inverse Weibull distributions. Besides the asymptotic and bootstrap confidence intervals, we derive HPD credible intervals when the shape parameter is known or unknown. We also propose the pivotal quantity and generalized confidence interval of reliability. We study the estimation of multicomponent stress–strength reliability using lower record values. Generalized, asymptotic, and bootstrap confidence intervals are derived using lower record values. We also derive confidence intervals of multicomponent stress–strength reliability assuming the shape parameters are different. We propose HPD credible intervals, generalized and bootstrap confidence intervals. Monte Carlo simulation is performed to compare the confidence intervals. Real data examples are presented to demonstrate the practicability of the confidence intervals.

Moment properties of lower record values from generalized inverse Weibull distribution and characterization

In this paper, the exact expressions as well as recurrence relations for single and product moments of the generalized lower record values from generalized inverse Weibull distribution are obtained. Further, the characterization of the given distribution is carried out through recurrence relations and conditional moment.

Inferences for generalized Topp-Leone distribution under dual generalized order statistics with applications to Engineering and COVID-19 data

This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record values. The Bayes estimate is derived with respect to a squared error loss function using gamma priors. The highest posterior density credible interval is computed based on the MH algorithm. Furthermore, the explicit expressions for single and product moments of dgos from this distribution are also derived. Based on order statistics and lower records, a simulation study is carried out to check the efficiency of these estimators. Two real life data sets, one is for order statistics and another is for lower record values have been analyzed to demonstrate how the proposed methods may work in practice.

Bayesian Estimation and Prediction for the Inverse Weibull Distribution Based on Lower Record Values

Bayesian Estimation and Prediction for the Inverse Weibull Distribution Based on Lower Record Values

Bayesian inference of Unit Gompertz distribution based on dual generalized order statistics

In this article, we consider the estimation problem of Unit Gompertz distribution with parameters α and β under the framework of dual generalized order statistics. This article is purely devoted to present the Bayesian view of estimation of Unit Gompertz distribution. For this purpose, we consider two widely popular approximation methods called Markov chain Monte Carlo and Lindley approximation methods. The results are derived under the symmetric (squared error) and asymmetric (Linear exponential and General entropy) loss functions. Since the order statistics and lower record values are the particular cases of the dual generalized order statistics, a simulation study is provided for order statistics and lower record values to observe the behavior of estimators. The average lengths of highest posterior density intervals of α, β, and R(t) are calculated for 95% confidence coefficient. Finally, real data applications are reported for lower record values and order statistics, separately, to show the practical aspects of the derived results.

Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.

Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values.

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function

The main contribution of this work is to develop a linear exponential loss function (LINEX) to estimate the scale parameter and reliability function of the inverse Weibull distribution (IWD) based on lower record values. We do this by merging a weight into LINEX to produce a new loss function called weighted linear exponential loss function (WLINEX). We then use WLINEX to derive the scale parameter and reliability function of the IWD. Subsequently, we discuss the balanced loss functions for three different types of loss function, which include squared error (SE), LINEX, and WLINEX. The majority of previous scholars determined the weighted balanced coefficients without mathematical justification. One of the main contributions of this work is to utilize nonlinear programming to obtain the optimal values of the weighted coefficients for balanced squared error (BSE), balanced linear exponential (BLINEX), and balanced weighted linear exponential (BWLINEX) loss functions. Furthermore, to examine the performance of the proposed methods—WLINEX and BWLINEX—we conduct a Monte Carlo simulation. The comparison is between the proposed methods and other methods including maximum likelihood estimation, SE loss function, LINEX, BSE, and BLINEX. The results of simulation show that the proposed models BWLINEX and WLINEX in this work have the best performance in estimating scale parameter and reliability, respectively, according to the smallest values of mean SE. This result means that the proposed approach is promising and can be applied in a real environment.

Transmuted Lower Record Type Fréchet Distribution with Lifetime Regression Analysis Based on Type I-Censored Data

This paper introduces a new lifetime distribution by mixing the first two lower record values and various distributional properties are examined. Statistical inference on distribution parameters are discussed with five estimators. A Monte Carlo simulation study is carried out to evaluate the risk behavior of these estimators for different sample of sizes. The distribution modeling analysis is provided based on real data to demonstrate the fitting ability of the proposed model. In addition, a lifetime regression model is described by re-parameterization on the log lifetimes. The superiority of proposed regression model is revealed in well-known models.

On estimation of stress-strength reliability using lower record values from odd generalized exponential: Exponential distribution

This research paper aims to find the estimated values closest to the true values of the reliability function under lower record values, and to know how to obtain these estimated values using point estimation methods or interval estimation methods. This helps researchers later in obtaining values of the reliability function in theory and then applying them to reality which makes it easier for the researcher to access the missing data for long periods such as weather. We evaluated the stress-strength model of reliability based on point and interval estimation for reliability under lower records by using Odd Generalize Exponential-Exponential distribution (OGEE) which has an important role in the lifetime of data. After that, we compared the estimated values of reliability with the real values of it. We analyzed the data obtained by the simulation method and the real data in order to reach certain results. The Numerical results for estimated values of reliability supported with graphical illustrations. The results of both simulated data and real data gave us the same coverage.