Estimation for the P(X > Y) of Lomax distribution under accelerated life tests.

The system or unit survives when strength is more significant than the stress enjoined. This procedure is usually used in many companies to test their product. The reliability or the quality of the scheme or component is described by the parameters of stress-strength reliability (R=P(X>Y)) where X denotes strength and Y indicates stress. In this article, we adopted the statistical inference of R while the two arbitrary factors X and Y are independent and approach the Lomax lifetime distribution with common scale parameters. Also, the strength and stress variables are subjected to a partial step-stress-quickened life experiment. The classical estimation and Bayes method create the point estimate of R. Confidence intervals of R are computed with asymptotic distribution, bootstrap technique, and Bayesian credible intervals. All results are evaluated and compared under an extensive simulation study. Finally, the lifetime data sets generated from the Lomax distribution are used to analyze the system's reliability by estimating R.

Modified generalized Weibull distribution: theory and applications.

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.

Analysis of Covid-19 data using discrete Marshall-Olkinin Length Biased Exponential: Bayesian and frequentist approach.

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.

A new asymmetric extended family: Properties and estimation methods with actuarial applications.

In the present work, a class of distributions, called new extended family of heavy-tailed distributions is introduced. The special sub-models of the introduced family provide unimodal, bimodal, symmetric, and asymmetric density shapes. A special sub-model of the new family, called the new extended heavy-tailed Weibull (NEHTW) distribution, is studied in more detail. The NEHTW parameters have been estimated via eight classical estimation procedures. The performance of these methods have been explored using detailed simulation results which have been ordered, using partial and overall ranks, to determine the best estimation method. Two important risk measures are derived for the NEHTW distribution. To prove the usefulness of the two actuarial measures in financial sciences, a simulation study is conducted. Finally, the flexibility and importance of the NEHTW model are illustrated empirically using two real-life insurance data sets. Based on our study, we observe that the NEHTW distribution may be a good candidate for modeling financial and actuarial sciences data.

Short-Term Prediction of COVID-19 Using Novel Hybrid Ensemble Empirical Mode Decomposition and Error Trend Seasonal Model.

In this article, a new hybrid time series model is proposed to predict COVID-19 daily confirmed cases and deaths. Due to the variations and complexity in the data, it is very difficult to predict its future trajectory using linear time series or mathematical models. In this research article, a novel hybrid ensemble empirical mode decomposition and error trend seasonal (EEMD-ETS) model has been developed to forecast the COVID-19 pandemic. The proposed hybrid model decomposes the complex, nonlinear, and nonstationary data into different intrinsic mode functions (IMFs) from low to high frequencies, and a single monotone residue by applying EEMD. The stationarity of each IMF component is checked with the help of the augmented Dicky-Fuller (ADF) test and is then used to build up the EEMD-ETS model, and finally, future predictions have been obtained from the proposed hybrid model. For illustration purposes and to check the performance of the proposed model, four datasets of daily confirmed cases and deaths from COVID-19 in Italy, Germany, the United Kingdom (UK), and France have been used. Similarly, four different statistical metrics, i.e., root mean square error (RMSE), symmetric mean absolute parentage error (sMAPE), mean absolute error (MAE), and mean absolute percentage error (MAPE) have been used for a comparison of different time series models. It is evident from the results that the proposed hybrid EEMD-ETS model outperforms the other time series and machine learning models. Hence, it is worthy to be used as an effective model for the prediction of COVID-19.

A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data.

The bivariate Poisson exponential-exponential distribution is an important lifetime distribution in medical data analysis. In this article, the conditionals, probability mass function (pmf), Poisson exponential and probability density function (pdf), and exponential distribution are used for creating bivariate distribution which is called bivariate Poisson exponential-exponential conditional (BPEEC) distribution. Some properties of the BPEEC model are obtained such as the normalized constant, conditional densities, regression functions, and product moment. Moreover, the maximum likelihood and pseudolikelihood methods are used to estimate the BPEEC parameters based on complete data. Finally, two data sets of real bivariate data are analyzed to compare the methods of estimation. In addition, a comparison between the BPEEC model with the bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) is considered.

Estimations of competing lifetime data from inverse Weibull distribution under adaptive progressively hybrid censored.

In real-life experiments, collecting complete data is time-, finance-, and resources-consuming as stated by statisticians and analysts. Their goal was to compromise between the total time of testing, the number of units under scrutiny, and the expenditures paid through a censoring scheme. Comparing failure-censored schemes (Type-Ⅱ and Progressive Type-Ⅱ) to Time-censored schemes (Type-Ⅰ), it's worth noting that the former is time-consuming and is no more suitable to be applied in real-life situations. This is the reason why the Type-Ⅰ adaptive progressive hybrid censoring scheme has exceeded other failure-censored types; Time-censored types enable analysts to accomplish their trials and experiments in a shorter time and with higher efficiency. In this paper, the parameters of the inverse Weibull distribution are estimated under the Type-Ⅰ adaptive progressive hybrid censoring scheme (Type-Ⅰ APHCS) based on competing risks data. The model parameters are estimated using maximum likelihood estimation and Bayesian estimation methods. Further, we examine the asymptotic confidence intervals and bootstrap confidence intervals for the unknown model parameters. Monte Carlo simulations are carried out to compare the performance of the suggested estimation methods under Type-Ⅰ APHCS. Moreover, Markov Chain Monte Carlo by applying Metropolis-Hasting algorithm under the square error of loss function is used to compute Bayes estimates and related to the highest posterior density. Finally, two data sets are studied to illustrate the introduced methods of inference. Based on our results, we can conclude that the Bayesian estimation outperforms the maximum likelihood estimation for estimating the inverse Weibull parameters under Type-Ⅰ APHCS.

Fusion-Based Deep Learning with Nature-Inspired Algorithm for Intracerebral Haemorrhage Diagnosis.

Natural computing refers to computational processes observed in nature and human-designed computing inspired by nature. In recent times, data fusion in the healthcare sector becomes a challenging issue, and it needs to be resolved. At the same time, intracerebral haemorrhage (ICH) is the injury of blood vessels on the brain cells, which is mainly liable for stroke. X-rays and computed tomography (CT) scans are widely applied for locating the haemorrhage position and size. Since manual segmentation of the CT scans by planimetry by the use of radiologists is a time-consuming process, deep learning (DL) is used to attain effective ICH diagnosis performance. This paper presents an automated intracerebral haemorrhage diagnosis using fusion-based deep learning with swarm intelligence (AICH-FDLSI) algorithm. The AICH-FDLSI model operates on four major stages namely preprocessing, image segmentation, feature extraction, and classification. To begin with, the input image is preprocessed using the median filtering (MF) technique to remove the noise present in the image. Next, the seagull optimization algorithm (SOA) with Otsu multilevel thresholding is employed for image segmentation. In addition, the fusion-based feature extraction model using the Capsule Network (CapsNet) and EfficientNet is applied to extract a useful set of features. Moreover, deer hunting optimization (DHO) algorithm is utilized for the hyperparameter optimization of the CapsNet and DenseNet models. Finally, a fuzzy support vector machine (FSVM) is applied as a classification technique to identify the different classes of ICH. A set of simulations takes place to determine the diagnostic performance of the AICH-FDLSI model using the benchmark intracranial haemorrhage data set. The experimental outcome stated that the AICH-FDLSI model has reached a proficient performance over the compared methods in a significant way.

Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications.

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah-Haghighi, and alpha-power inverse-Weibull distributions.

Objective bayesian analysis for multiple repairable systems.

This article focus on the analysis of the reliability of multiple identical systems that can have multiple failures over time. A repairable system is defined as a system that can be restored to operating state in the event of a failure. This work under minimal repair, it is assumed that the failure has a power law intensity and the Bayesian approach is used to estimate the unknown parameters. The Bayesian estimators are obtained using two objective priors know as Jeffreys and reference priors. We proved that obtained reference prior is also a matching prior for both parameters, i.e., the credibility intervals have accurate frequentist coverage, while the Jeffreys prior returns unbiased estimates for the parameters. To illustrate the applicability of our Bayesian estimators, a new data set related to the failures of Brazilian sugar cane harvesters is considered.

Stress-Strength Reliability for Exponentiated Inverted Weibull Distribution with Application on Breaking of Jute Fiber and Carbon Fibers.

For the first time and by using an entire sample, we discussed the estimation of the unknown parameters θ 1, θ 2, and ß and the system of stress-strength reliability R=P(Y < X) for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when X and Y are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real-life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena.

Thermally Enhanced Darcy-Forchheimer Casson-Water/Glycerine Rotating Nanofluid Flow with Uniform Magnetic Field.

This numerical study aims to interpret the impact of non-linear thermal radiation on magnetohydrodynamic (MHD) Darcy-Forchheimer Casson-Water/Glycerine nanofluid flow due to a rotating disk. Both the single walled, as well as multi walled, Carbon nanotubes (CNT) are invoked. The nanomaterial, thus formulated, is assumed to be more conductive as compared to the simple fluid. The properties of effective carbon nanotubes are specified to tackle the onward governing equations. The boundary layer formulations are considered. The base fluid is assumed to be non-Newtonian. The numerical analysis is carried out by invoking the numerical Runge Kutta 45 (RK45) method based on the shooting technique. The outcomes have been plotted graphically for the three major profiles, namely, the radial velocity profile, the tangential velocity profile, and temperature profile. For skin friction and Nusselt number, the numerical data are plotted graphically. Major outcomes indicate that the enhanced Forchheimer number results in a decline in radial velocity. Higher the porosity parameter, the stronger the resistance offered by the medium to the fluid flow and consequent result is seen as a decline in velocity. The Forchheimer number, permeability parameter, and porosity parameter decrease the tangential velocity field. The convective boundary results in enhancement of temperature facing the disk surface as compared to the ambient part. Skin-friction for larger values of Forchheimer number is found to be increasing. Sufficient literature is provided in the introduction part of the manuscript to justify the novelty of the present work. The research greatly impacts in industrial applications of the nanofluids, especially in geophysical and geothermal systems, storage devices, aerospace engineering, and many others.

A new extended rayleigh distribution with applications of COVID-19 data.

This paper aims to model the COVID-19 mortality rates in Italy, Mexico, and the Netherlands, by specifying an optimal statistical model to analyze the mortality rate of COVID-19. A new lifetime distribution with three-parameter is introduced by a combination of Rayleigh distribution and extended odd Weibull family to produce the extended odd Weibull Rayleigh (EOWR) distribution. This new distribution has many excellent properties as simple linear representation, hazard rate function, and moment generating function. Maximum likelihood, maximum product spacing and Bayesian estimation methods are applied to estimate the unknown parameters of EOWR distribution. MCMC method is used for the Bayesian estimation. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. Also, data analysis for the real data of mortality rate is considered.

Inferences for Exponentiated Gamma Constant-Stress Partially Accelerated Life Test Model Based on Generalized Type-I Hybrid Censored Data.

In this paper, the exponentiated gamma distribution (EGD) with generalized Type-I hybrid censored data under constant-stress partially accelerated life test (CSPALT) model is considered. The Bayesian and E-Bayesian estimation methods, as well as the maximum likelihood estimation method, are discussed for the parameter of the distribution and the acceleration factor. The E-Bayesian and Bayesian estimates are derived by using the squared error loss (SEL) and the LINEX loss functions. The MCMC method is applied for deriving the Bayesian and then E-Bayesian estimates. Moreover, a real data set is given for the illustrative purpose. After all, an evaluation is performed for the results of the proposed methods.