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Abstract This paper introduces a novel approach to life-testing using Extended Dagum (EXD) percentiles within the framework of group inspection plans. The methodology focuses on optimizing sample sizes and analyzing termination time ratios to enhance the reliability of quality control procedures. By leveraging the flexibility of the EXD distribution, the proposed approach accurately models complex survival data, accommodating heavy-tailed characteristics often encountered in practice. The study presents a detailed analysis of optimal sample sizes and the critical termination time ratios that balance producer and consumer risks. Through comprehensive simulations and real applications, the paper demonstrates the effectiveness of the proposed methodology in ensuring robust and efficient life-testing strategies, offering valuable insights for practitioners in industries such as manufacturing, engineering, and reliability analysis.

This study introduces a novel family of probability distributions called the ”tangent exponential-G family,” which is derived using trigonometric transformations of the exponential distribution. The significance of this research lies in developing new statistical models with versatile hazard functions, including j-shaped, S-shaped, increasing, and bathtub shapes. The primary aim is to construct and analyze the properties of this new distribution family. We utilized the exponential distribution function and applied the tangent transformation to develop the tangent exponential-G family. Key statistical properties and characteristics of this family are explored. Parameter estimation is performed using different estimation methods, and its accuracy is confirmed through simulation studies, which show reduced biases and mean square errors with increasing sample sizes. We tested the proposed distribution with real-world data sets to demonstrate practical applicability. Comparative analyses using model selection criteria and goodness-of-fit tests reveal that the tangent exponential-G family and its sub-model outperform compared to existing models, indicating its robustness and utility in statistical modeling.

It is a deep-rooted and already observed reality that probabilistic models play an important role in describing and explaining the events/situations under consideration. Focusing attention on the fundamental role and applicability of the probabilistic models, this article considers the development of a new probability model derived through the implementation of a trigonometric function. The suggested model is named as a new cosine flexible Weibull (NCF-Weibull) distribution. This model is accomplished by exploiting the cosine functional approach. Some statistical characteristics of the NCF-Weibull distribution are given. Alongside, the estimates of the NCF-Weibull model are also obtained. Besides them, a simulation study for different settings of the parameter values of the NCF-Weibull model is also provided. Through the simulation study it is evidenced that the estimators of the NCF-Weibull distribution consistently perform well in terms of stability, consistency, and efficiency. Finally, the optimality of the NCF-Weibull distribution is judged by using two applications from different sectors. Based on five evaluation criteria alongside the p-value, the NCF-Weibull distribution shows optimal performances for both data sets.

Abstract This research introduces a novel two-parameter distribution, the power-modified XLindley distribution, developed through the application of power transformation techniques to the existing modified XLindley distribution. This new distribution enhances flexibility and adaptability in statistical modeling. We conduct a thorough examination of its statistical properties, exploring its potential to improve data fitting and modeling accuracy. To assess the effectiveness of the model, we employ multiple estimation techniques and evaluate their performance through extensive simulation experiments. Our findings indicate that the maximum product of the spacings method is particularly effective for parameter estimation. To demonstrate the practical utility of the proposed model, we apply it to two real-world datasets: one related to flood data and the other to reliability engineering. The results underscore the distribution’s superior ability to capture the characteristics of these datasets compared to existing models, highlighting its significance for applications in natural disaster analysis and reliability studies.

This paper presents a new probability distribution called the DUS Lindley distribution, created by applying the DUS transformation to the traditional Lindley distribution. The study provides an in-depth analysis of the distribution's statistical properties. These properties include a variety of statistical measures such as the probability density function, cumulative distribution function, failure rate, survival function, reverse hazard function, Mills ratio, mean residual life, mean past life, moments, conditional moments, characteristic function, order statistics, entropy measures, likelihood ratio test and Lorenz and Bonferroni curves. Parameter estimation is performed using several methods including weighted least squares, maximum likelihood estimation, Cramer-Von Mises estimation, least squares and Anderson-Darling estimation. The paper also explores the estimation of system reliability and evaluates the performance of maximum likelihood estimators through simulation studies across different sample sizes. Finally, the DUS Lindley distribution is applied to two real-world datasets, demonstrating a better fit than other well-known distributions.

Recent teaching trends are increasingly integrating diverse multimedia and computer-aided practices to enhance representation and understanding. Leveraging data-focused strategies, these methods are further refined with artificial intelligence and decision-making techniques. To improve data handling in multimedia-based teaching representation, this article introduces an integrated data representation model aided by regression learning (IDR-RL). The proposed model satisfies the data required for different teaching methods/ subjects based on curriculum and student requirements. The data integration from different sources is performed using checksum assessment. The checksum assessment for data provides precise assimilation and content-related data-to-visual representation. In this representation, the checksums are verified for their linearity, wherein the saturation/ threshold factors are identified, and data integration is recommended. This recommendation is performed as the decision-making for preventing paused representation in live teaching sessions. The checksums are used for content coherency and complete data representations to prevent time lags in teaching. The proposed model’s performance is verified through data handling rate, integration ratio, pause time, representation time lag, and failures.

This paper presents a novel two-parameter distribution derived from the Rayleigh distribution, thoroughly investigating its essential mathematical properties. We employ estimation techniques to determine the proposed distribution's estimated parameters. Through extensive simulation studies, we analyze and evaluate the asymptotic behavior of the model estimators. Furthermore, we calculate various actuarial measures to highlight the practical utility of the proposed distribution in actuarial science. To further substantiate the applicability of our distribution, we perform a comprehensive regression analysis. The practical relevance of the proposed distribution is demonstrated by modeling a lifetime dataset from the insurance field, where it exhibits a superior fit compared to existing distributions. The findings suggest that the new distribution significantly improves modeling capabilities, making it a valuable tool for theoretical research and practical applications in fields requiring accurate lifetime data modeling.

Abstract This research commences a unit statistical model named power new power function distribution, exhibiting a thorough analysis of its complementary properties. We investigate the advantages of the new model, and some fundamental distributional properties are derived. The study aims to improve insight and application by presenting quantitative and qualitative perceptions. To estimate the three unknown parameters of the model, we carefully examine various methods: the maximum likelihood, least squares, weighted least squares, Anderson–Darling, and Cramér-von Mises. Through a Monte Carlo simulation experiment, we quantitatively evaluate the effectiveness of these estimation methods, extending a robust evaluation framework. A unique part of this research lies in developing a novel regressive analysis based on the proposed distribution. The application of this analysis reveals new viewpoints and improves the benefit of the model in practical situations. As the emphasis of the study is primarily on practical applications, the viability of the proposed model is assessed through the analysis of real datasets sourced from diverse fields.

In this article, we offer simple random sampling (SRS) based efficient class of estimators of population mean Y¯ utilizing additional information. The expression of the mean square error of the proposed class of estimators is deduced up to first degree approximation. The efficiency conditions are established which are enhanced numerically utilizing a simulation study consummated over symmetrical and asymmetrical populations. Real data sets are also utilized to exemplify the suggested estimators. The numerical findings are appeared rather acceptable demonstrating better advancement over the ordinary estimators.

This study considers one of the partially accelerated life testing models, mainly a constant-stress approach with unified hybrid censored data. The data represents the lifetime of units following the exponentiated gamma distribution (EGD). The estimation techniques for the parameter of EGD and the acceleration factor are discussed, along with the maximum likelihood estimation technique, the Bayesian and E-Bayesian estimation. Utilizing the squared error loss (SEL) and LINEX loss functions, the E-Bayesian and Bayesian estimates are generated. For deriving the estimates of Bayesian and E-Bayesian approaches, we use the MCMC method. Real-world data is also provided for illustration. Furthermore, unified hybrid censoring schemes (HCSs) are examined to determine their effectiveness in the light of the results. In the end, we compare among the proposed methods during their findings. The study's findings demonstrate how well the suggested techniques work when utilizing unified HCS. The study also makes clear how important it is to adopt the CSPALT model, as it yields more failed things in a shorter amount of time than items with typical use situations. In conclusion, it is suggested that this research be used to tasks like industrial product reliability testing.

The study and investigation of the behavior of monetary phenomena is an interesting subject for actuaries and practitioners. In the recent age and development in the monetary and financial phenomena, cryptocurrency has gained much attention from actuaries. Over the past decade, several research studies have emerged on modeling and forecasting cryptocurrency exchange rates. This paper also contributes to the modeling of cryptocurrency exchange rates using a new version of the Logistic distribution, namely, a new cotangent-Logistic distribution. The mathematical properties and estimators of the new cotangent-logistic distribution's parameters are obtained. We illustrate the new cotangent-Logistic distribution using two financial data sets representing the log-returns of the Bitcoin and Ethereum prices. We compare the new cotangent-Logistic distribution with the baseline Logistic distribution and its modified version. Using the p-value and three other statistical tests, we show that the new cotangent-Logistic distribution repeatedly provides the optimal fit to cryptocurrency exchange rates.

In the sample survey theory, the crux of survey practitioners is to provide “accurate” estimators of the parameter of choice. The conventional theory depends on the regression/difference estimators as they correspond to the best linear unbiased (BLU) estimators. This paper suggests some optimal classes of estimators by modifying the conventional estimators under stratified ranked set sampling (SRSS). The characteristics of the suggested estimators are established to the first-order approximation. The performance of the suggested class of estimators under SRSS has been theoretically and experimentally shown to be superior to traditional estimators, particularly regression (BLU) estimators.

This article proposes and discusses a novel approach for generating trigonometric G-families using hybrid generalizers of distributions. The proposed generalizer is constructed by utilizing the tangent trigonometric function and distribution function of base model G(x). The newly proposed family of uni-variate continuous distributions is named the “Lomax Tangent Generalized Family of Distributions (LT-G)” and structural-mathematical-statistical properties are derived. Some special and sub-models of the proposed family are also presented.A Weibull-based model, ‘The Lomax Tangent Weibull (LT-W) Distribution,” is discussed and the plots of density (pdf) and hazard (hrf) functions are also explained. Model parameter estimates are estimated by employing the maximum likelihood estimation (MLE) procedure. The accuracy of the MLEs is evaluated through Monte Carlo simulation. Last but not least, to demonstrate the flexibility and potential of the proposed distribution, two actual hydrological and strength data sets are analyzed. The obtained results are compared with well-known, competitive, and related existing distributions.

The paper introduces the hybrid odd exponential-Φ (HOE-Φ) family, a novel framework for generating a continuous distribution characterized by an additional parameter. The extensive statistical properties of this family are derived and explored in detail. Parameter estimation is performed using the maximum likelihood estimation technique. The efficacy and versatility of the proposed model are demonstrated through a comparative analysis involving two distinct real-world datasets.

Probability distributions play useful and meaningful roles in sports sciences and biomedical sectors. Probability distributions can be used to model and predict the chances of injuries and recovery time after the injuries. We propose and implement a new method to introduce new probability distributions. The new method is named a new updated-V family, as it can be used to increase/update the flexibility of the modified and traditional probability models. Based on the new updated-V method, a new extension of the Weibull model, namely, a new updated Weibull model is proposed. Statistical properties of the new updated-Weibull model, such as (i) quantile function, (ii) heavy-tailed properties (iii) rth moment, (iv) probability weighted moments, and (i) moment generating functions are presented. For the new updated-V distributions, the estimators are derived. The assessment of the new updated-V distribution estimators is done via a simulation study. A practical application related to the re-injury rate data is considered for the establishment of the applicability of the new updated Weibull distribution.

Russia and Ukraine got into an armed conflict on 24th February 2022. In addition, the World Health Organisation still warns of a fast growth in infections and deaths. Infectious disease remains a serious issue in Ukraine and poorly governed cities, such as those in armed conflicts. During this period of security instability, the coronavirus situation in Ukraine is alarming and needs more attention. In this context, our focus in the current work is to model COVID-19 spread risk from Ukrainian international refugees in neighboring countries. This study aims to estimate the number of daily coronavirus cases among Ukrainian international refugees for informed decisions for the pandemics' spread risk. For that reason, we used “Coronavirus Pandemic (COVID-19)” data from “Our World in Data” (from 2020-03-03 to 2022-02-22) and the data about Ukrainian International Refugees provided by United Nations High Commissioner for Refugees related (from 2022-02-22 to 2022-03-11). We performed ARIMA, TBATS, and ETS and selected the best model. Through a cross-validation process, the findings revealed that around 6 individuals [95% CI: 5%–7%] over 10,000 Ukrainian international refugees are likely COVID-19 cases. ARIMA is the best model to fit the Ukrainian daily number of cases among the refugees fleeing the crisis. On average, they are daily 100 possible COVID-19 cases among Ukrainian international refugees and authorities and humanitarian actors need be informed decisions to control the pandemic and support refugees effectively.

Abstract This article presents and investigates a modified version of the Weibull distribution that incorporates four parameters and can effectively represent a hazard rate function with a shape resembling a bathtub. Its significance in the fields of lifetime and reliability stems from its ability to model both increasing and decreasing failure rates. The proposed distribution encompasses several well-known models such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh, and modified Weibull distributions. The paper derives key mathematical statistics of the proposed distribution, including the quantile function, moments, moment-generating function, and order statistics density. Various mathematical properties of the proposed model are established, and the unknown parameters of the distribution are estimated using different estimation techniques. Furthermore, the effectiveness of these estimators is assessed through numerical simulation studies. Finally, the paper applies the new model and compares it with various existing distributions by analyzing two real-life time data sets.

Abstract Evaluating the lifespan distribution of highly reliable commodities under regular use is exceedingly difficult, time consuming, and extremely expensive. As a result of its ability to provide more failure data faster and at a lower experimental cost, accelerated life testing has become increasingly important in life testing studies. In this article, we concentrate on parametric inference for step stress partially life testing utilizing multiple censored data based on the Tampered Random Variable model. Under normal stress circumstances, the lifespan of the experimental units is assumed to follow the Nadarajah–Haghighi distribution, with and being the shape and scale parameters, respectively. Maximum likelihood estimates for model parameters and acceleration factor are developed using multiple censored data. We build asymptotic confidence intervals for the unknown parameters using the observed Fisher information matrix. To demonstrate the applicability of the different methodologies, an actual data set based on the timings of subsequent failures of consecutive air conditioning system failures for each member of a Boeing 720 jet aircraft fleet is investigated. Finally, thorough simulation studies utilizing various censoring strategies are performed to evaluate the estimate procedure performance. Several sample sizes were studied in order to investigate the finite sample features of the considered estimators. According to our numerical findings, the values of mean squared errors and average asymptotic confidence intervals lengths drop as sample size increases. Furthermore, when the censoring level is reduced, the considered estimates of the parameters approach their genuine values.

Abstract The paper presents a novel statistical approach for analyzing the daily coronavirus case and fatality statistics. The survival discretization method was used to generate a two-parameter discrete distribution. The resulting distribution is referred to as the "Discrete Marshall–Olkin Length Biased Exponential (DMOLBE) distribution". Because of the varied forms of its probability mass and failure rate functions, the DMOLBE distribution is adaptable. We calculated the mean and variance, skewness, kurtosis, dispersion index, hazard and survival functions, and second failure rate function for the suggested distribution. The DI index demonstrates that the proposed model can represent both over-dispersed and under-dispersed data sets. We estimated the parameters of the DMOLBE distribution. The behavior of ML estimates is checked via a comprehensive simulation study. The behavior of Bayesian estimates is checked by generating 10,000 iterations of Markov chain Monte Carlo techniques, plotting the trace, and checking the proposed distribution. From simulation studies, it was observed that the bias and mean square error decreased with an increase in sample size. To show the importance and flexibility of DMOLBE distribution using two data sets about deaths due to coronavirus in China and Pakistan are analyzed. The DMOLBE distribution provides a better fit than some important discrete models namely the discrete Burr-XII, discrete Bilal, discrete Burr-Hatke, discrete Rayleigh distribution, and Poisson distributions. We conclude that the new proposed distribution works well in analyzing these data sets. The data sets used in the paper was collected from 2020 year.

This study focuses on a novel family of distributions inspired by the hyperbolic sine function. The Rayleigh distribution is the base model for the newly formed family of distributions known as the new hyperbolic Sine-Rayleigh distribution. The recommended distribution’s distinct structural traits have been examined. The behaviors of the distributional functions of the proposed model are depicted in several figures. The maximum likelihood estimation procedure is employed to estimate the specified distribution parameters. A simulation study was carried out to examine and evaluate the behavior of the estimators. Moreover, the efficacy of the specified distribution is supported by realistic data sets pertaining to engineering science.

The World Health Organization (WHO) announced on March 11, 2020, that COVID-19 could be considered a pandemic. This epidemic has become a huge issue for academics, doctors, healthcare providers, epidemiologists, and decision-makers alike. Motivated by studying natural phenomena, we concentrated on making a statistical model capable of fitting natural pandemics into the whole world. In this manuscript, we introduced a new novel distribution called the Inverse Power Haq (IPH) distribution. We created this distribution due to its formidable merits. We introduced its statistical properties and plotted its probability density function (PDF), cumulative distribution function (CDF), and hazard rate function (HRF). We utilized classical estimation techniques to determine the parameters for the suggested distribution. In the paper's conclusion, we performed a data analysis, applying the distribution to COVID-19 infection in Kuwait for practical purposes. Our analysis demonstrated the superior performance of the proposed distribution compared to its competitors, establishing it as the most suitable choice for modeling COVID-19 data in patients of different ages. Lastly, the conclusion section includes a summary of our overall findings and conclusions.

We aim in this paper to propose a novel class of distributions that was created by merging the Topp-Leone distribution and the Generated families of Kumaraswamy and Marshall-Olkin. Its cumulative distribution function characterizes it and includes rational and polynomial functions. In particular, the following desirable properties of the new family are presented: Shannon entropy, order statistics, the quantile power series, and several associated measures and functions. Then, using a specific family member identified before, we create a parametric statistical model with the basic distribution being the inverse exponential distribution. Finally, a thorough investigation has been made to implement this new distribution with three data sets: the glass fibers data set, the glass Alumina data set and the hailing times data set. In comparison to six prominent competitors, the new model performs favorably on all statistical tests and criteria that were examined.

The study’s major goal is to design a superior creative distribution by using the Kumaraswamy-G family of distributions to power Frechet distribution. The Kumaraswamy power Frechet distribution (KPFD) with four parameters is the full name of the revolutionary model. The distribution’s probability density function may take numerous forms and graphs and can be used to describe complicated data sets efficiently. Several features of the new distribution are obtained, including dependability, hazard rate, quantile, and moments. The estimation of the unknown parameters of KPFD are provided using the KPFD maximum likelihood estimation technique. Furthermore, a study was performed using the Monte Carlo simulation approach to test estimator accuracy regarding average bias (AB) and mean square error (MSE). Last but not least, two genuine data sets are supplied to compare the proposed model to existing models.

We introduce a new model called the length-biased exponential distribution which become a fascinating new model in a number of research domains in recent years. By adding an extra shape parameter, a new generalised form that is coupled to the length-biased exponential distribution addressed in this work may be constructed, enhancing its utility. The new distribution is known as the new extension length-biased exponential distribution (NELBE). Its density function, as well as its survival and hazard rate curves, are all shown graphically. The study presented the quantile function, linear representations, and some other properties. We displayed and graphed the shapes of the distribution functions. When it came time to calculate the distribution parameters, we employed a total of six distinct estimating strategies. In order to compare and draw conclusions about the performance of the different estimators, a thorough numerical analysis was done. Here, two real data set on COVID-19 mortality rate was examined to show how adaptable and practical the suggested distribution is.

In this article, the odd Lomax Gompertz distribution has been introduced, which is derived by modifying the Gompertz distribution to serve as a baseline model in the odd generalized Lomax distribution. The newly proposed model offers enhanced flexibility and provides a promising alternative for modeling lifetime data. This study seeks to establish a solid theoretical foundation for its application through the exploration of several properties, such as non-central moments, stochastic orderings quantile function, and entropy measure, for the new model. Additionally, by conducting simulation analysis, the performance of the various estimation methods is being assessed, which enables the identification of the most reliable approach for estimating the unknown parameters of the newly developed model. The simulation analysis of the two-risk metrics, namely, value at risk and expected shortfall, revealed the ability of the distribution to capture diverse failure rate patterns, which makes it particularly relevant for assessing financial risks. Finally, the suggested model is practiced to two real-life datasets to provide the compelling evidence of superior flexibility and practical versatility compared to existing models in the literature.

In this paper, a new flexible two-parameter family of distributions is introduced. Some mathematical properties, such as asymptotic behavior, moments, stochastic order, entropy, and quantile function, are examined. A special case of this family is introduced called Gemeay–Zeghdoudi distribution. The unknown parameters of the Gemeay–Zeghdoudi distribution are estimated via many estimators. The efficiency of the estimators is compared with a Monte Carlo simulation. The applicability of the new distribution is illustrated by the annual maximum flood and survival times of patients with breast cancer real data analyses.

The two-parameter classical Weibull distribution is commonly implemented to cater for the product’s reliability, model the failure rates, analyze lifetime phenomena, etc. In this work, we study a novel version of the Weibull model for analyzing real-life events in the sports and medical sectors. The newly derived version of the Weibull model, namely, a new cosine-Weibull (NC-Weibull) distribution. The importance of this research is that it suggests a novel version of the Weibull model without adding any additional parameters. Different distributional properties of the NC-Weibull distribution are obtained. The maximum likelihood approach is implemented to estimate the parameters of the NC-Weibull distribution. Finally, three applications are analyzed to prove the superiority of the NC-Weibull distribution over some other existing probability models considered in this study. The first and second applications, respectively, show the mortality rates of COVID-19 patients in Italy and Canada. Whereas, the third data set represents the injury rates of the basketball players collected during the 2008–2009 and 2018–2019 national basketball association seasons. Based on four selection criteria, it is observed that the NC-Weibull distribution may be a more suitable model for considering the sports and healthcare data sets.

This paper is concerned with making statistical inference on extended inverse Weibull (EXIW) distribution under type-II censored sample distribution. This distribution posses a lot of marvels statistical properties, such as linear representation, and many other properties among them the incomplete moment which has been provided in addition to the stress strength reliability function, and moments. To conduct a thorough study of this distribution, we estimated its parameters using both classical and non-classical techniques on both progressive censored and complete data. In order to find the best and efficient method of estimation we made a simulation study and using its results we mentioned which method is the best. We used modified algorithms to find the fitting of the data to the EXIW distribution. In the end, but certainly not least, we developed an application by making use of the EXIW distribution in order to evaluate its superiority in comparison to its competitors.

This paper presents a novel probability distribution, namely the new XLindley distribution, derived from a unique combination of exponential and gamma distributions through a special mixture formulation. The study extensively investigates the mathematical properties of the proposed distribution, including but not limited to the moment generation function, moments of different orders, mode identification, and the quantile function. Furthermore, the research employs a Monte Carlo simulation to assess and compare the performance of various estimators in estimating the unknown parameter of the new XLindley distribution. These estimators are carefully evaluated and analyzed in terms of their efficiency and accuracy, providing valuable insights into the practical application of the new distribution in statistical modeling and data analysis contexts. The voltage and failure time data in the field of engineering are used to model the proposed distribution. The new model is compared with many current distributions such as Xlindley, gamma, Weibull, exponential, Lindley, Shanker, Akash, Zeghdoudi, Chris-Jerry, and Xgamma. Among all models, it is concluded that the new one-parameter distribution performed the best in modeling based on criteria such as the Akaike information criterion, Bayesian information criterion, and others. The real data results show that the proposed distribution exhibits greater flexibility and improved goodness of fit compared to alternative distributions. The new XLindley distribution could be useful in modeling real-life data and may warrant further exploration in future research. Overall, this study contributes to the field of probability distributions and provides new insights for statistical modeling.

The initial COVID-19 vaccinations were created and distributed to the general population in 2020 thanks to emergency authorization and conditional approval. Consequently, numerous countries followed the process that is currently a global campaign. Taking into account the fact that people are being vaccinated, there are concerns about the effectiveness of that medical solution. Actually, this study is the first one focusing on how the number of vaccinated people might influence the spread of the pandemic in the world. From the Global Change Data Lab "Our World in Data", we were able to get data sets about the number of new cases and vaccinated people. This study is a longitudinal one from 14/12/2020 to 21/03/2021. In addition, we computed Generalized log-Linear Model on count time series (Negative Binomial distribution due to over dispersion in data) and implemented validation tests to confirm the robustness of our results. The findings revealed that when the number of vaccinated people increases by one new vaccination on a given day, the number of new cases decreases significantly two days after by one. The influence is not notable on the same day of vaccination. Authorities should increase the vaccination campaign to control well the pandemic. That solution has effectively started to reduce the spread of COVID-19 in the world.

In this paper, we introduce a new class of statistical models to deal with the data sets in the sports and health sectors. The new class is called, a novel exponent power-Y (NovEP-Y) family of distributions. By implementing the NovEP-Y approach, a new model, namely, a novel exponent power-Weibull (NovEP-Weibull) distribution is introduced. Some distributional properties of the NovEP-Y family such as identifiability, order statistics, quantile function, and moments are obtained. The maximum likelihood estimators of the parameters are also derived. Furthermore, a brief Monto Carlo simulation study is conducted to evaluate the performances of the estimators. To show the applicability of the NovEP-Weibull model, two data sets from the sports and health sciences are considered. The first data set represents the time-to-even data collected from different football matches during the period 1964–2018. Whereas, the second data set is taken from the health sector, representing the survival times of the COVID-19 infected patients. Based on some well-known statistical tests, it is observed that the NovEP-Weibull model is a very competitive distribution for modeling the data sets in the sports and health sectors.

The aim of this work is to develop a new outstanding lifetime distribution, dubbed the power Bilal (PB) distribution. Both of the probability distribution function (pdf) and the cumlative distribution function (cdf) of the PB distribution have a simple forms. The suggested distribution’s moments, incomplete moments as well as the quantile function are deduced and acquired in explicit forms as a result of its simple forms. Seven estimation methods for estimating the PB distribution parameters are mentioned, and numerical simulations are used to compare the proposed approaches using partial and overall ranks. According to the simulation results of this work, the maximum likelihood estimators are advised to be the best estimation method for estimating the parameters of the PB distribution, when the data genrated from the PB distribution. We shows the importance and flexibility of the PB distribution by comparing it to other existing competing distributions using two different real data sets from COVID-19 mortality rates of two countries.

The log-normal, log-logistic and Weibull distributions are commonly utilized to model survival data. Unimodal (or non-monotone) failure rate functions are modeled using the log-normal and the log-logistic families, whereas monotone failure rate functions are modeled using the Weibull family. The growing availability of survival data with a variety of features encourages statisticians to propose more flexible parametric models that can accommodate both monotone (increasing or decreasing), and non-monotone (unimodal or bathtub) failure rate functions. One such model is the generalized log-logistic distribution which not only accommodates unimodal failure rates but also allows for a monotone and non-monotone failure rate functions. This distribution has shown to have a lot of potential in univariate analysis of survival data. However, many studies are primarily concerned with determining the link between survival time and one or more explanatory variables. This leads to the study of hazard-based regression models in survival and reliability analysis, which can be formulated in a variety of ways. One such method concerns formulating hazard-based regression models for the accelerated failure time (AFT) family of continuous probability distributions. The log-logistic, Weibull and log-normal distributions are the most widely utilized this framework. In this paper, we show that the generalized log-logistic distribution is closed under the accelerated failure time framework. We then formulate an accelerated failure time model based on the generalized log-logistic distribution. Furthermore, we show parameter estimation for the model using Bayesian and frequentist approaches. An extensive simulation study is conducted to illustrate the inferential properties of the proposed model, more specifically, the tendency to recover the baseline hazard shapes, parameter estimation, as well as the effect of censoring proportions on inference. The simulation results demonstrate that the generalized log-logistic accelerated failure time model can be capable of modeling survival data with various hazard rate shapes. Finally, a real-life survival data relating to larynx-cancer patients was used.

Generating new statistical models is one of the most commonly used methods to represent real-life occurrences. Sometimes, with a known distribution, it may not be possible to represent a scenario, so we may consider generalization to incorporate more variance in the data. In this article, we offer a modified cubic transmuted-G family of distributions to enrich the members of the second-order transmuted distributions. By utilizing this modified class of distributions, we build a new distribution entitled the modified cubic transmuted Rayleigh distribution, along with its distributional features, estimate, associated inference, and real-life applications.

Here, we present a new bounded distribution known as the power Lambert uniform distribution, and we deduce some of its statistical properties such as quantile function, moments, incomplete moments, mean residual life and mean inactivity time, Lorenz, Bonferroni, and Zenga curves, and order statistics. We presented different shapes of the probability density function and the hazard function of the proposed model. Eleven traditional methods are used to estimate its parameters. The behavior of these estimators is investigated using simulation results. Some actuarial measures are derived mathematically for our proposed model. Some numerical computations for these actuarial measures are given for some choices of parameters and significance levels. A new quantile regression model is constructed based on the new unit distribution. The maximum likelihood estimation method is used to estimate the unknown parameters of the regression model. Furthermore, the usability of the new distribution and regression models is demonstrated with the COVID-19 and educational datasets, respectively.

The modern trend in distribution theory is to propose hybrid generators and generalized families using existing algebraic generators along with some trigonometric functions to offer unique, more flexible, more efficient, and highly productive G-distributions to deal with new data sets emerging in different fields of applied research. This article aims to originate an odd sine generator of distributions and construct a new G-family called "The Odd Lomax Trigonometric Generalized Family of Distributions". The new densities, useful functions, and significant characteristics are thoroughly determined. Several specific models are also presented, along with graphical analysis and detailed description. A new distribution, "The Lomax cosecant Weibull" (LocscW), is studied in detail. The versatility, robustness, and competency of the LocscW model are confirmed by applications on hydrological and survival data sets. The skewness and kurtosis present in this model are explained using modern graphical methods, while the estimation and statistical inference are explored using many estimation approaches.

This paper addresses asymmetric flexible two-parameter exponential model called the weighted exponential (WDEx) distribution. Some of its basic mathematical features are evaluated. Its hazard rate accommodates upside-down bathtub, decreasing, decreasing-constant, increasing, and increasing-constant shapes. Five actuarial indicators are studied. We utilize nine classical and Bayesian approaches of estimation for estimating the WDEx parameters. We provide a detailed simulation study to explore and assess the asymptotic behaviors of these estimators. Two approximation methods called the Markov chain Mont Carlo and Tierney and Kadane are applied to obtain the Bayesian estimates. The efficiency and applicability of the WDEx distribution are explored by modeling a lifetime data set from insurance field, showing that the WDEx distribution provides a superior fit over its competing exponential models such as the beta-exponential, Harris extend-exponential, Marshall–Olkin exponential, Marshall–Olkin alpha-power exponential, gamma Weibull, and exponentiated-Weibull distributions.

The core objective of this work is to predict stock market indices’ using autoregressive integrated moving average (ARIMA), artificial neural network (ANN) and their combination in the form of ARIMA-ANN. Financial data are, in fact, trendy, noisy and highly volatile. To tackle their chaotic nature and forecast the three considered stock markets, namely Nasdaq stock exchange, United States, Nikkei stock exchange, Japan, and France stock exchange data (CAC 40 index), we use novel approaches. The data are taken from the Yahoo Finance website for the period from 4 January 2010 to 20 August 2021. To assess the relative predictive effectiveness of the selected tools, the dataset was divided into two distinct subsets: 75% of the data was allocated for training purposes, while the remaining 25% was reserved for testing. The empirical results suggest that ARIMA-ANN produces more accurate forecasts than the separate components of all stock markets. In light of this, it may be inferred that the combining tool is more effective in analyzing financial data and provides a more accurate comparative prediction.

Background. A country’s agriculture reflects a backbone and performs a vital part in the betterment of the economy and individuals. Facts and figures of the agriculture sector offer a solid foundation and factual pathway intended for upcoming decisions in favor of a country. Accordingly, the probability models have a more significant influence not only in reliability engineering, hydrology, ecology, and medicine but also in agriculture sciences. Objective. The primary objective of this study is to propose a reliable and efficient model for pearl millet yield analysis, thereby empowering decision-makers to make informed decisions about their farming practices. With the successful implementation of this model, farmers can potentially increase their pearl millet yield, leading to higher incomes and improved livelihoods for the rural population of Pakistan. Model. This study proposes a novel probability model, namely, the alpha transformed odd exponential power function (ATOE-PF) distribution, for analyzing pearl millet yield in Punjab, Pakistan. Data. For data collection, two secondary data sets are explored that are electronically available on the site of the Directorate of Agriculture (Economics and Marketing) Punjab, Lahore, Pakistan. Results. The maximum likelihood estimation technique is used for estimating the model parameters. For the selection of a better fit model, we follow some accredited goodness of fit tests. The efficiency and applicability of the ATOE-PF distribution are discussed over the province of Punjab (with RMSE = 4.9176) and Pakistan (with RMSE = 4.5849). Better estimates and closest fit to data among the well-established neighboring models offer robust evidence in support of ATOE-PF distribution as well.

This paper provides a novel model that is more relevant than the well-known conventional distributions, which stand for the two-parameter distribution of the lifetime modified Kies Topp-Leone (MKTL) model. Compared to the current distributions, the most recent one gives an unusually varied collection of probability functions. The density and hazard rate functions exhibit features, demonstrating that the model is flexible to several kinds of data. Multiple statistical characteristics have been obtained. To estimate the parameters of the MKTL model, we employed various estimation techniques, including maximum likelihood estimators (MLEs) and the Bayesian estimation approach. We compared the traditional reliability function model to the fuzzy reliability function model within the reliability analysis framework. A complete Monte Carlo simulation analysis is conducted to determine the precision of these estimators. The suggested model outperforms competing models in real-world applications and may be chosen as an enhanced model for building a statistical model for the COVID-19 data and other data sets with similar features.

In this paper, we introduced a novel general two-parameter statistical distribution which can be presented as a mix of both exponential and gamma distributions. Some statistical properties of the general model were derived mathematically. Many estimation methods studied the estimation of the proposed model parameters. A new statistical model was presented as a particular case of the general two-parameter model, which is used to study the performance of the different estimation methods with the randomly generated data sets. Finally, the COVID-19 data set was used to show the superiority of the particular case for fitting real-world data sets over other compared well-known models.

We introduced a brand-new member of the family that is going to be referred to as the New Power Topp-Leone Generated (NPTL-G). This new member is one of a kind. Given the major functions that created this new member, important mathematical aspects are discussed in as much detail as possible. We derived some functions for the new one, included the Rényi entropy, the qf, series development, and moment weighted probabilities. Moreover, to estimate the values of the parameters of our model that were not known, we employed the maximum likelihood technique. In addition, two actual datasets from the real world were investigated in order to bring attention to the possible applications of this novel distribution. This new model performs better than three key rivals based on the measurements that were collected.

During the course of this research, we came up with a brand new distribution that is superior; we then presented and analysed the mathematical properties of this distribution; finally, we assessed its fuzzy reliability function. Because the novel distribution provides a number of advantages, like the reality that its cumulative distribution function and probability density function both have a closed form, it is very useful in a wide range of disciplines that are related to data science. One of these fields is machine learning, which is a sub field of data science. We used both traditional methods and Bayesian methodologies in order to generate a large number of different estimates. A test setup might have been carried out to assess the effectiveness of both the classical and the Bayesian estimators. At last, three different sets of Covid-19 death analysis were done so that the effectiveness of the new model could be demonstrated.

In this paper, fuzzy stress strengths RF=P(Y≺X) and traditional stress strengths R=P(Y

Using a progressive Type-I censoring technique, this article will explore how to estimate unknown parameters of the alpha power exponential distribution (APED) (Type-I PCS). The squared error loss function and the LINEX loss function are used to get the maximum likelihood estimate as well as the Bayesian estimation of the unknown parameters, respectively. It was our intention to use the Markov chain Monte Carlo method in conjunction with the Bayes estimation strategy. We are able to calculate the approximately accurate confidence intervals for the parameters whose values are unknown. In addition to this, we discussed the estimation challenges of reliability and the hazard rate function of the APED while using Type-I PCS, as well as the approximate confidence intervals that relate to these problems. In the last step, the theoretical findings that were acquired are evaluated and compared with the distributions of all of its rivals by making use of two actual datasets that represent the disciplines of engineering and medicine.

The objective of this study is to construct a new distribution known as the weighted Burr-Hatke distribution (WBHD). The PDF and CDF of the WBHD are derived in a closed form. Moments, incomplete moments, and the quantile function of the proposed distribution are derived mathematically. Eleven estimate techniques for estimating the distribution parameters are discussed, and numerical simulations are utilised to evaluate the various approaches using partial and overall rankings. According to the findings of this study, it is recommended that the maximum product of spacing (MPSE) estimator of the WBHD is the best estimator according to overall rank table. The actuarial measurements were derived to the suggested distribution. By contrasting the WBHD with other competitive distributions using two different actual data sets collected from the COVID-19 mortality rates, we show the importance and flexibility of the WBHD.

The extended reduced Kies distribution (ExRKD), which is an asymmetric flexible extension of the reduced Kies distribution, is the subject of this research. Some of its most basic mathematical properties are deduced from its formal definitions. We computed the ExRKD parameters using eight well-known methods. A full simulation analysis was done that allows the study of these estimators’ asymptotic behavior. The efficiency and applicability of the ExRKD are investigated via the modeling of COVID-19 and milk data sets, which demonstrates that the ExRKD delivers a better match to the data sets when compared to competing models.

Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm transformed-inverse Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution.

The power XLindley (PXL) distribution is introduced in this study. It is a two-parameter distribution that extends the XLindley distribution established in this paper. Numerous statistical characteristics of the suggested model were determined analytically. The proposed model’s fuzzy dependability was statistically assessed. Numerous estimation techniques have been devised for the purpose of estimating the proposed model parameters. The behaviour of these factors was examined using randomly generated data and developed estimation approaches. The suggested model seems to be superior to its base model and other well-known and related models when applied to the COVID-19 data set.