On Modeling Concrete Compressive Strength Data Using Laplace Birnbaum-Saunders Distribution Assuming Contaminated Information

Compressive strength is a well-known measurement to evaluate the endurance of a given concrete mixture to stress factors, such as compressive loads. A suggested approach to assess compressive strength of concrete is to assume that it follows a probability model from which its reliability is calculated. In reliability analysis, a probability distribution’s reliability function is used to calculate the probability of a specimen surviving to a certain threshold without damage. To approximate the reliability of a subject of interest, one must estimate the corresponding parameters of the probability model. Researchers typically formulate an optimization problem, which is often nonlinear, based on the maximum likelihood theory to obtain estimates for the targeted parameters and then estimate the reliability. Nevertheless, there are additional nonlinear optimization problems in practice from which different estimators for the model parameters are obtained once they are solved numerically. Under normal circumstances, these estimators may perform similarly. However, some might become more robust under irregular situations, such as in the case of data contamination. In this paper, nine frequentist estimators are derived for the parameters of the Laplace Birnbaum-Saunders distribution and then applied to a simulated data set and a real data set. Afterwards, they are compared numerically via Monte Carlo comparative simulation study. The resulting estimates for the reliability based on these estimators are also assessed in the latter study

On Entropy Estimation of Inverse Weibull Distribution under Improved Adaptive Progressively Type-II Censoring with Applications

This article utilizes improved adaptive progressively Type-II censored data to estimate the entropy of the inverse Weibull distribution. Rényi, q, and Shannon entropy measurements are used to define entropy to achieve this objective. Both point and interval estimations of the entropy quantities are investigated through the maximum likelihood and maximum product of spacing methods. Two parametric bootstrap confidence intervals based on the two estimation techniques are also considered for the various entropy measures. A Monte Carlo simulation study is conducted to investigate how estimates behave at various sample sizes and different censoring schemes based on some statistical measurements. The simulations demonstrate that, as anticipated, when the sample size grows, the estimation accuracy also grows. Furthermore, they show that the estimated entropy measures get closer to the actual entropy values when the censoring level decreases. For purposes of explanation, two applications to actual datasets are taken into consideration. The results verified that the adaptive or improved adaptive progressive censoring schemes give more information about data than the conventional progressive censoring scheme in terms of minimum entropy measures

Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring

This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood method is also considered. The point estimates and the approximate confidence intervals of the unknown parameters are obtained using the two methods. In addition, two parametric bootstrap confidence intervals are discussed based on both estimation methods. Extensive simulation studies are conducted by considering different censoring schemes to examine the efficiency of each estimation method. Finally, two real data sets for oil breakdown times of insulating fluid and minority electron mobility are analyzed to show the applicability of the different methods. Moreover, the reliability function and the mean time-to-failure under the normal use condition are estimated using both methods. Based on Monte Carlo simulation outcomes and real data analysis, we recommend using the maximum product of spacing to evaluate both the point and interval estimates for the modified Kies exponential distribution parameters in the presence of constant-stress partially accelerated Type-II censored data

Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring

This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood method is also considered. The point estimates and the approximate confidence intervals of the unknown parameters are obtained using the two methods. In addition, two parametric bootstrap confidence intervals are discussed based on both estimation methods. Extensive simulation studies are conducted by considering different censoring schemes to examine the efficiency of each estimation method. Finally, two real data sets for oil breakdown times of insulating fluid and minority electron mobility are analyzed to show the applicability of the different methods. Moreover, the reliability function and the mean time-to-failure under the normal use condition are estimated using both methods. Based on Monte Carlo simulation outcomes and real data analysis, we recommend using the maximum product of spacing to evaluate both the point and interval estimates for the modified Kies exponential distribution parameters in the presence of constant-stress partially accelerated Type-II censored data

The generalized linear exponential distribution

This paper deals with a new generalization of the linear exponential distribution. This distribution is called the generalized linear exponential distribution (GLED). Some statistical properties such as moments, modes and quantiles are derived. The failure rate function and the mean residual lifetime are also discussed. The maximum likelihood estimators of the parameters are obtained using a simulation study. Real data are used to determine whether the GLED is better than other well-known distributions in modeling lifetime data or not.Linear exponential distribution Generalized linear exponential distribution Failure rate Mean residual lifetime

On Modeling Cancer and Tuberculosis Data Using the Birnbaum–Saunders Lifetime Model Established on a Logistic Kernel

Due to their importance in representing, explaining, and analyzing phenomena, statistical lifetime distributions are widely used in science. As a result, this paper discusses a modern lifetime model called Birnbaum–Saunders logistic distribution. This distribution extends the Birnbaum–Saunders distribution, as it has proven to be characterized by great flexibility in data modeling in practice. Different features of this distribution have been discussed. The parameters of the model are estimated using the maximum likelihood and modified moment estimation methods. To evaluate the performance of the methods, a simulation study with data contamination scenarios is presented. Finally, the new model’s flexibility is tested using real datasets

Modeling Climate data using the Quartic Transmuted Weibull Distribution and Different Estimation Methods

Researchers from various fields of science encounter phenomena of interest, and they seek to model the occurrences scientifically. An important approach of performing modeling is to use probability distributions. Probability distributions are probabilistic models that have many applications in different research areas, including, but not limited to, environmental and financial studies. In this paper, we study a quartic transmuted Weibull distribution from a general quartic transmutation family of distributions as a generalization and an alternative to the well-known Weibull distribution. We also investigate the practical application of this generalization by modeling climate-related data sets and check the goodness-of-fit of the proposed model. The statistical properties of the proposed model, which includes non-central moments, generating functions, survival function, and hazard function, are derived. Different estimation methods to estimate the parameters of the proposed quartic transmuted distribution: the maximum likelihood estimation method, the maximum product of spacings method, two least-squares-based methods, and three goodness-of-fit-based estimation methods. Numerical illustration and an extensive comparative Monte Carlo simulation study are conducted to investigate the performance of the estimators of the considered inferential methods. Regarding estimation methods, simulation outcomes indicated that the maximum likelihood estimation (MLE), Anderson-Darling estimation (ADE) and right Anderson-Darling (RADE) methods in general outperformed the other considered methods in terms of estimation efficiency for large sample size, while all considered estimation methods performed almost same in terms of goodness-of-fit regardless the values of shape and transmuted parameters. Two real-life data sets are used to demonstrate the suggested estimation methods, the applicability and flexibility of the proposed distribution compared to Weibull, transmuted Weibull, and cubic transmuted Weibull distributions. Weighted least squares estimation (WLSE) and least squares estimation (LSE) methods provided best model fitting estimates of the proposed distribution for Wheaton River and rainfall data respectively. The proposed quartic transmuted Weibull distribution provide significantly improved fit for the two datasets as compared with other distributions