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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.

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.

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.

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.

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.

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.

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.