REVSTAT-Statistical Journal

Control Monitoring Schemes for Monitoring Percentiles of Generalized Exponential Distribution with Hybrid Censoring

Shovan Chowdhury — 2025-02-05

In this article, a parametric bootstrap control monitoring scheme equivalently known as control chart, is proposed for process monitoring of percentiles of the generalized exponential distribution for type-I hybrid censored data assuming in-control parameters to be unknown. Similar schemes can be derived for type-I and type-II censored data as a special case of the proposed censoring scheme. Monte Carlo simulations are carried out for various combinations of percentiles, false-alarm rates and sample sizes to evaluate the in-control performance of the proposed scheme in terms of average run lengths. The out-of-control behavior and performance of the scheme is thoroughly investigated for several choices of shifts in the parameters of the distribution. Conventional Shewhart-type scheme is also proposed under the same set-up asymptotically and compared with bootstrap scheme using a skewed data set. The chart under hybrid censoring scheme is found to be more effective than the same under type-I and type-II censoring schemes in terms of magnitude and speed of detection of out-of-control signals. Finally, an application of the proposed scheme is shown from clinical practice.

Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application

Kousik Maiti — 2025-02-05

The purpose of the present paper is two-fold. First, we consider the estimation of the unknown model parameters and the reliability characteristics of a gamma-mixed Rayleigh distribution when a progressively type-II censored sample (PT-IICS) is available. The sufficient condition for the existence and uniqueness of the maximum likelihood estimates (MLE) is obtained. We compute MLEs using the expectation-maximization (EM) algorithm. Asymptotic confidence intervals are constructed. For comparison purposes, confidence intervals using bootstrap-p and bootstrap-t methods are also constructed. Bayes estimates are derived with respect to the squared error, LINEX, and the entropy loss functions. Two approximation techniques (Lindley and importance sampling) are used for the computation of the Bayes estimates. Further, the highest posterior density (HPD) credible intervals are derived using the importance sampling method. Second, we consider the problem of Bayesian prediction. Prediction estimates and the associated prediction equal-tail intervals under one-sample and two-sample frameworks are obtained. A simulation study is conducted the comparison the methods of estimation and prediction. Finally, a real dataset is considered and analyzed for the purpose of illustration.

On a Characterization of Exponential and Double Exponential Distributions

Reza Rastegar — 2025-02-05

Recently, G. Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev’s theorem by relaxing a restriction on the sign of mixture coefficients and, in addition, obtain a similar characterization for the Laplace family of distributions.

Optimal Imputation Methods under Stratified Ranked Set Sampling

Shashi Bhushan — 2025-02-05

It is long familiar that the stratified ranked set sampling (SRSS) is more efficient than ranked set sampling (RSS) and stratified random sampling (StRS). The existence of missing values alter the final inference of any study. This paper is fundamental effort to suggest some combined and separate imputation methods in presence of missing data under SRSS. It has been shown that the proposed imputation methods become superior than the mean imputation method, ratio imputation method, Diana and Perri (2010) type imputation method and Sohail et al. (2018) type imputation methods. A simulation study is administered over two hypothetically drawn asymmetric populations.

Data Analytics and Distribution Function Estimation via Mean Absolute Deviation: Nonparametric Approach

Elsayed A. H. Elamir — 2025-02-05

Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster a quick and a deep understanding of the data as an important basis for successful data analytics. Furthermore, new nonparametric approaches for estimating the cumulative distribution function based on the mean absolute deviation function are proposed. These new approaches are meant to be a general nonparametric class that includes the empirical distribution function as a special case. Simulation study reveals that the Richardson extrapolation approach has a major improvement in terms of average squared errors over the classical empirical estimators and has comparable results with smooth approaches such as cubic spline and constrained linear spline for practically small samples. The properties of the proposed estimators are studied. Moreover, the Richardson approach has been applied to real data analysis and has been used to estimate the hazardous concentration five percent.

Survival Copula Entropy and Dependence in Bivariate Distributions

S.M. Sunoj — 2025-01-05

In the present work we propose survival copula entropy as an alternative to Shannon entropy, cumulative residual entropy and copula entropy measures in computing the uncertainty in bivariate populations. We examine the relationships between the various measures. The properties of survival copula entropy are discussed, especially its applications to ascertain the nature and extent of uncertainty among copulas.

Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution

Varun Agiwal — 2025-02-05

In this article, we propose and study a new three-parameter heavy-tailed distribution that unifes the Burr type XII and power inverted Topp-Leone distributions in an original manner. This unification is made through the use of a simple 'shift parameter'. Among its interesting functionalities, it exhibits possibly decreasing and unimodal probability density and hazard rate functions. We examine its quantile function, stochastic dominance, ordinary moments, weighted moments, incomplete moments, and stress-strength reliability cofficient. Then, the classical and Bayesian approaches are developed to estimate the model and stress strength reliability parameters. Bayes estimates are obtained under the squared error and entropy loss functions. Simulated data are considered to point out the performance of the derived estimates based on the mean squared error. In the final part, the potential of the new model is exemplified by the analysis of two engineering data sets, showing that it is preferable to other reputable and comparable models.

Stochastic Generator of a New Family of Lifetime Distributions with Illustration

Amjad Al-Nasser — 2025-02-05

In this article, a new family of lifetime distributions is introduced to help researchers model different types of data sets. Furthermore, the maximum likelihood method was used in estimating the model's parameters. Some structural properties of the distribution have been derived and studied. These are density function, distribution function, and reliability function, hazard rate function, moments, moment generating function, entropies, order statistics, Bonferroni and Lorenz curves. Simulation method was used to investigate the behaviors of the parameters of the proposed distribution; the results showed that the mean square error and standard error for the chosen parameter values decrease as the sample size increases. The proposed distribution was tested on real-life data, the results showed that the ET-exponential distribution performed better than other well-known distributions in modeling data. The results also showed that the distribution can be used as an alternative model in modeling lifetime processes.