A Generalization of Generalized Gamma Distributions

<p>For the first time, a new generalization of generalized gamma distribution called the modified generalized gamma distribution has been introduced to provide greater flexibility in modeling data from a practical viewpoint. The new distribution generalizes some recently introduced generalizations of the gamma distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean deviation, mean residual lifetime and expression of the entropies are derived. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Two real data sets have been analyzed to show how the proposed models work in practice.</p

Inference on Constant Stress Accelerated Life Tests Under Exponentiated Exponential Distribution

Accelerated life tests have become increasingly important because of highercustomer expectations for better reliability, more complicated products withmore components, rapidly changing technologies advances, and the clear needfor rapid product development. Hence, accelerated life tests have been widelyused in manufacturing industries, particularly to obtain timely informationon the reliability. Maximum likelihood estimation is the starting point whenit comes to estimating the parameters of the model. In this paper, besides themethod of maximum likelihood, nine other frequentist estimation methodsare proposed to obtain the estimates of the exponentiated exponential distribution parameters under constant stress accelerated life testing. We considertwo parametric bootstrap confedence intervals based on different methods ofestimation. Furthermore, we use the different estimates to predict the shapeparameter and the reliability function of the distribution under the usualconditions. The performance of the ten proposed estimation methods isevaluated via an extensive simulation study. As an empirical illustration,the proposed estimation methods are applied to an accelerated life test dataset

A New Unit Distribution: Properties, Inference, and Applications

We propose a new bounded distribution called the Marshall{Olkin reducedKies distribution, which is a competitive model to the generalized beta, Kumaraswamy and beta distributions. It is able to model both negative andpositive skewed data. Eight classical estimation methods are used to estimateits parameters. A simulation study is conducted to compare the performanceof the dierent estimators. The performance ordering of these estimators isexplored using partial and overall ranks to determine the best estimationmethod. Two COVID-19 data sets on to recovering and death rates in Spainare analyzed to show the exibility of the new distribution to model suchdata. The expected values of the rst and last order statistics are used toestimate the minimum and maximum recovery and death rates

A New Unit Distribution: Properties, Inference, and Applications

We propose a new bounded distribution called the Marshall{Olkin reducedKies distribution, which is a competitive model to the generalized beta, Kumaraswamy and beta distributions. It is able to model both negative andpositive skewed data. Eight classical estimation methods are used to estimateits parameters. A simulation study is conducted to compare the performanceof the dierent estimators. The performance ordering of these estimators isexplored using partial and overall ranks to determine the best estimationmethod. Two COVID-19 data sets on to recovering and death rates in Spainare analyzed to show the exibility of the new distribution to model suchdata. The expected values of the rst and last order statistics are used toestimate the minimum and maximum recovery and death rates

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Summary Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. Methods We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung’s disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. Findings We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung’s disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in lowincome countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. Interpretation Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between lowincome, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030

Bayesian Estimation Using Expected LINEX Loss Function: A Novel Approach with Applications

The loss function plays an important role in Bayesian analysis and decision theory. In this paper, a new Bayesian approach is introduced for parameter estimation under the asymmetric linear-exponential (LINEX) loss function. In order to provide a robust estimation and avoid making subjective choices, the proposed method assumes that the parameter of the LINEX loss function has a probability distribution. The Bayesian estimator is then obtained by taking the expectation of the common LINEX-based Bayesian estimator over the probability distribution. This alternative proposed method is applied to estimate the exponential parameter by considering three different distributions of the LINEX parameter, and the associated Bayes risks are also obtained in consequence. Extensive simulation studies are conducted in order to compare the performance of the proposed new estimators. In addition, three real data sets are analyzed to investigate the applicability of the proposed results. The results of the simulation and real data analysis show that the proposed estimation works satisfactorily and performs better than the conventional standard Bayesian approach in terms of minimum mean square error and Bayes risk

Statistical Analysis of Inverse Weibull Constant-Stress Partially Accelerated Life Tests with Adaptive Progressively Type I Censored Data

In life-testing investigations, accelerated life testing is crucial since it reduces both time and costs. In this study, constant-stress partially accelerated life tests using adaptive progressively Type I censored samples are taken into account. This is accomplished under the assumption that the lifespan of products under normal use conditions follows the inverse Weibull distribution. In addition to using the maximum likelihood approach, the maximum product of the spacing procedure is utilized to obtain the point and interval estimates of the model parameters as well as the acceleration factor. Employing the premise of independent gamma priors, the Bayes point estimates using the squared error loss function and the Bayes credible intervals are obtained based on both the likelihood and product of spacing functions via the Markov chain Monte Carlo technique. To assess the effectiveness of the various approaches, a simulation study is used because it is not possible to compare the findings theoretically. To demonstrate the applicability of the various approaches, two real datasets for the lifetime of micro-droplets in the ambient environment and light-emitting diode failure data are investigated. Based on the numerical results, to estimate the parameters and acceleration factor of the inverse Weibull distribution based on the suggested scheme with constant-stress partially accelerated life tests, it is recommended to utilize the Bayesian estimation approach

A New Exponential Distribution to Model Concrete Compressive Strength Data

Concrete mixtures can be developed to deliver a broad spectrum of mechanical and durability properties to satisfy the configuration conditions of construction. One technique for evaluating the compressive strength of concrete is to suppose that it pursues a probabilistic model from which it is reliability estimated. In this paper, a new technique to generate probability distributions is considered and a new three-parameter exponential distribution as a new member of the new family is presented in detail. The proposed distribution is able to model the compressive strength of high-performance concrete rather than some other competitive models. The new distribution delivers decreasing, increasing, upside-down bathtub and bathtub-shaped hazard rates. The maximum likelihood estimation approach is used to estimate model parameters as well as the reliability function. The approximate confidence intervals of these quantities are also obtained. To assess the performance of the point and interval estimations, a simulation study was conducted. We demonstrate the performance of the offered new distribution by investigating one high-performance concrete compressive strength dataset. The numerical outcomes showed that the maximum likelihood method provides consistent and asymptotically unbiased estimators. The estimates of the unknown parameters as well as the reliability function perform well as sample size increases in terms of minimum mean square error. The confidence interval of the reliability function has an appropriate length utilizing the delta method. Moreover, the real data analysis indicated that the new distribution is more suitable when compared to some well-known and some recently proposed distributions to evaluate the reliability of concrete mixtures

Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data

In reliability analysis and life testing studies, the experimenter is frequently interested in studying a specific risk factor in the presence of other factors. In this paper, the estimation of the unknown parameters, reliability and hazard functions of alpha power exponential distribution is considered based on progressively Type-II censored competing risks data. We assume that the latent cause of failures has independent alpha power exponential distributions with different scale and shape parameters. The maximum likelihood method is considered to estimate the model parameters as well as the reliability and hazard rate functions. The approximate and two parametric bootstrap confidence intervals of the different estimators are constructed. Moreover, the Bayesian estimation method of the unknown parameters, reliability and hazard rate functions are obtained based on the squared error loss function using independent gamma priors. To get the Bayesian estimates as well as the highest posterior credible intervals, the Markov Chain Monte Carlo procedure is implemented. A comprehensive simulation experiment is conducted to compare the performance of the proposed procedures. Finally, a real dataset for the relapse of multiple myeloma with transplant-related mortality is analyzed

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