Search

Limitations inherent to existing statistical distributions in capturing the complexities of real-world data often necessitate the development of novel models. This paper introduces the new exponential generalized inverse generalized Weibull (NEGIGW) distribution. The NEGIGW distribution boasts significant flexibility with symmetrical and asymmetrical shapes, allowing its hazard rate function to be adapted to many failure patterns observed in various fields such as medicine, biology, and engineering. Some statistical properties of the NEGIGW distribution, such as moments, quantile function, and Renyi entropy, are studied. Three methods are used for parameter estimation, including maximum likelihood, maximum product of spacing, and percentile methods. The performance of the estimation methods is evaluated via Monte Carlo simulations. The NEGIGW distribution excels in its ability to fit real-world data accurately. Five medical and engineering datasets are applied to demonstrate the superior fit of NEGIGW distribution compared to competing models. This compelling evidence suggests that the NEGIGW distribution is promising for lifetime data analysis and reliability assessments across different disciplines. [ABSTRACT FROM AUTHOR]

In parametric statistical modeling, it is essential to create generalizations of current statistical distributions that are more flexible when modeling actual data sets. Therefore, this study introduces a new generalized lifetime model named the odd Weibull Inverse Gompertz distribution (OWIG). The OWIG is derived by combining the odd Weibull family of distributions with the inverse Gompertz distribution. Essential statistical properties are discussed, including reliability functions, moments, Rényi entropy, and order statistics. The proposed OWIG is particularly significant as its hazard rate functions exhibit various monotonic and nonmonotonic shapes. This enables OWIG to model different hazard behaviors more commonly observed in natural phenomena. OWIG's parameters are estimated and its flexibility in predicting unique symmetric and asymmetric patterns is shown by analyzing real-world applications from psychology, environmental, and medical sciences. The results demonstrate that the proposed OWIG is an excellent candidate as it provides the most accurate fits to the data compared with some competing models. [ABSTRACT FROM AUTHOR]

Statistical probability distributions are commonly used by data analysts and statisticians to describe and analyze their data. It is possible in many situations that data would not fit the existing classical distributions. A new distribution is therefore required in order to accommodate the complexities of different data shapes and enhance the goodness of fit. A novel model called the new generalized exponentiated Fréchet–Weibull distribution is proposed in this paper by combing two methods, the transformed transformer method and the new generalized exponentiated method. This novel modeling approach is capable of modeling complex data structures in a wide range of applications. Some statistical properties of the new distribution are derived. The parameters have been estimated using the method of maximum likelihood. Then, different simulation studies have been conducted to assess the behavior of the estimators. The performance of the proposed distribution in modeling has been investigated by means of applications to three real datasets. Further, a new regression model is proposed through reparametrization of the new generalized exponentiated Fréchet–Weibull distribution using the log-location-scale technique. The effectiveness of the proposed regression model is also investigated with two simulation studies and three real censored datasets. The results demonstrated the superiority of the proposed models over other competing models. [ABSTRACT FROM AUTHOR]

A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models. [ABSTRACT FROM AUTHOR]

This paper introduces a novel alpha power exponentiated Weibull-Pareto distribution based on the alpha power transformation. We derive several properties of the new distribution, including moments, quantile function, mean residual life, mean waiting time, and order statistics. Estimating model parameters is performed using the method of maximum likelihood. Then, for the purpose of evaluating the effectiveness of the estimates, we conduct some simulation studies. Finally, we demonstrate the superiority of this new model by analyzing three real-life data sets. [ABSTRACT FROM AUTHOR]

Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions. [ABSTRACT FROM AUTHOR]

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and COVID-19 data under classical and Bayesian perspectives based on type-II censored data. We derive several properties of the new distribution such as moments, incomplete moments, mean deviation, average lifetime, mean residual lifetime, Rényi entropy, Shannon entropy, and order statistics of the proposed distribution. Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model. Bayes estimators of the unknown parameters of the model are obtained under symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions using gamma priors for both the shape and the scale parameters. Furthermore, approximate confidence intervals and Bayes credible intervals (CIs) are also obtained. Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimators and Bayes estimators with respect to their estimated risk. The flexibility and importance of the proposed distribution are illustrated by means of four real datasets. [ABSTRACT FROM AUTHOR]

Objectives: To investigate the effectiveness of wet cupping as alternative treatment on reducing bone pain and built a model that predicts the level of improvement for patients who suffer from bone pain. Methods: This retrospective study was conducted on 289 patients referred from specialty clinics to Prophetic Medicine Clinics (PMC) between September 2013 and August 2015. The effectiveness of cupping is assessed on patients with bone pain who were redirected to PMC, King Abdulaziz University Hospital, Jeddah, Saudi Arabia. An artificial neural network (ANN) method was used to propose a model that predicts levels of improvement for patients suffering from bone pain. Therefore, a random sample of 90% of the data was used to build the ANN model and tested by the remaining 10%. Inferential statistics were conducted to study relations and compare blood tests before and after treatment. Results: Out of 289 patients suffering from bone pain, more than 11% were completely cured, and 55% improved after wet cupping treatment sessions. The proposed ANN model showed a good performance with more than 72% accuracy. In addition, the statistical analysis showed a significant improvement for most blood tests. Conclusion: Wet cupping has positive effects on reducing bone pain. We recommend the use of an ANN model in PMC to predict whether patients will benefit from the treatment to reduce pain. This is a recommendation for further study not a conclusion. [ABSTRACT FROM AUTHOR]

The authors, therefore, acknowledge with thanks DSR for technical and financial support. The correct Funding statement is: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. [Extracted from the article]

In the process of identifying potential anticancer agents, the ability of a new agent is tested for cytotoxic activity against a panel of standard cancer cell lines. The National Cancer Institute (NCI) present the cytotoxic profile for each agent as a set of estimates of the dose required to inhibit the growth of each cell line. The NCI estimates are obtained from a linear interpolation method applied to the dose-response curves. In this paper non-linear fits are proposed as an alternative to interpolation. This is illustrated with data from two agents recently submitted to NCI for potential anticancer activity. Fitting of individual non-linear curves proved difficult, but a non-linear mixed model applied to the full set of cell lines overcame most of the problems. Two non-linear functional forms were fitted using random effect models by both maximum likelihood and a full Bayesian approach. Model-based toxicity estimates have some advantages over those obtained from interpolation. They provide standard errors for toxicity estimates and other derived quantities, allow model comparisons. Examples of each are illustrated. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis. [ABSTRACT FROM AUTHOR]

In this article, we introduce the exponentiated Fréchet-G family of distributions. Several models of the introduced exponentiated Fréchet-G family are presented. The proposed family is precisely more flexible and effective in modeling complex data and is instrumental in reliability analysis. It covers a wide variety of shapes, such as unimodal, reverse J, right-skewed, symmetrical, and asymmetrical shapes. Various structural mathematical properties, such as the quantile, moment, incomplete moment, entropy, and order statistics, are derived. The parameters are evaluated using a parametric estimation method. The performance and flexibility of the exponentiated Fréchet-G family are analyzed via a simulation and two applications; one deals with reliability data, and the other deals with medical data. [ABSTRACT FROM AUTHOR]

This article introduces the odds exponential-Pareto IV distribution, which belongs to the odds family of distributions. We studied the statistical properties of this new distribution. The odds exponential-Pareto IV distribution provided decreasing, increasing, and upside-down hazard functions. We employed the maximum likelihood method to estimate the distribution parameters. The estimators performance was assessed by conducting simulation studies. A new log location-scale regression model based on the odds exponential-Pareto IV distribution was also introduced. Parameter estimates of the proposed model were obtained using both maximum likelihood and jackknife methods for right-censored data. Real data sets were analyzed under the odds exponential-Pareto IV distribution and log odds exponential-Pareto IV regression model to show their flexibility and potentiality. [ABSTRACT FROM AUTHOR]

Pareto type II distribution has been studied from many statisticians due to its important role in reliability modelling and lifetime testing. In this article, we introduce two bivariate Pareto Type II distributions; one is derived from copula and the other is based on mixture and copula. Parameter Estimates of the proposed distribution are obtained using the maximum likelihood method. The performance of the proposed bivariate distributions is examined using a simulation study. Finally, we analyze one data set under the proposed distributions to illustrate their flexibility for real-life applications. [ABSTRACT FROM AUTHOR]