A new modified Kies Fréchet distribution: Applications of mortality rate of Covid-19

A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling

In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the Kavya-Manoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.

Generalized exponentiated unit Gompertz distribution for modeling arthritic pain relief times data: classical approach to statistical inference

Arthritis is the tenderness and swelling of one or more of the joints. Arthritis therapies are directed mainly at reducing symptoms and improving quality of life. In this article, we introduced a novel four parametric model known as generalized exponentiated unit Gompertz (GEUG) for modeling a clinical trial data which represent the relief or relaxing times of arthritic patients receiving a fixed dosage of certain medication. The key feature of such novel model is the addition of new tuning parameters to unit Gompertz (UG) with the intention of increasing versatility of the UG model. We have derived and studied different statistical and reliable attributes, along with moments and associated measures, uncertainty measures, moments generating functions, complete/incomplete moments, quantile function, survival and hazard functions. A comprehensive simulation analysis is implemented to evaluate the effectiveness of estimation of distribution parameters using numerous well-known classical approaches, like maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson Darling estimation (ADE), right tail Anderson darling estimation (RTADE), and Cramer-Von Mises estimation (CVME). Finally, using a relief time's data on arthritis pain show adaptability of suggested model. The results revealed that it might fit better than other relative models.

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.

Modeling the Amount of Carbon Dioxide Emissions Application: New Modified Alpha Power Weibull-X Family of Distributions

The use of statistical distributions to model life phenomena has received considerable attention in the literature. Recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in environmental sciences. Among them, the Weibull distribution is one of the most well-known models that can be used very effectively for modeling data in the fields of pollution and gas emissions, to name a few. In this paper, we introduce a family of distributions, which we call the modified Alpha-Power Weibull-X family of distributions. Based on the proposed family, we introduce a new model with five parameters, the modified Alpha-Power Weibull–Weibull distribution. Some mathematical properties were determined. Bayesian and maximum likelihood estimates for the model parameters were derived. The MLEs, bootstrap and Bayesian HPD credibility intervals for the unknown parameters were performed. A Monte Carlo simulation study was performed to evaluate the performance of the estimates. A simulation study was performed based on the parameters of the proposed model. An application to the carbon dioxide emissions dataset was performed to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the model. For this data set, the proposed model is compared with the modified alpha power Weibull exponential distribution and the two-parameter Weibull distribution. To show which of the competing distributions is the best, we draw on certain analytical tools such as the Kolmogorov–Smirnov test. Based on these analytical measures, we found that the new model outperforms the competing models.

Acceptance sampling plans for the three-parameter inverted Topp-Leone model

The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp-Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp-Leone (TPITL) distribution. The power inverted Topp-Leone and the inverted Topp-Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp-Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.

Interval Estimation for the Two-Parameter Exponential Distribution Based on the Upper Record Values

Using the data for upper record values, the interval estimation for the scale parameter of two-parameter exponential distribution is presented. In addition, two methods for the joint confidence region of two parameters are proposed. In terms of confidence region area, the simulation comparison of two methods of the confidence region is performed in this paper. The criterion of minimum confidence region area is used to obtain the optimal method of the confidence region. To illustrate our proposed interval estimation methods, one biometrical example is used and the corresponding confidence interval length and confidence region area are also calculated. Our research topic is related to the asymmetrical probability distributions and applications across disciplines.

Modeling the multifractal dynamics of COVID-19 pandemic

To describe the COVID-19 pandemic, we propose to use a mathematical model of multifractal dynamics, which is alternative to other models and free of their shortcomings. It is based on the fractal properties of pandemics only and allows describing their time behavior using no hypotheses and assumptions about the structure of the disease process. The model is applied to describe the dynamics of the COVID-19 pandemic from day 1 to day 699 from the beginning of the pandemic. The calculated parameters of the model accurately determine the parameters of the trend and the large jump in daily diseases in this time interval. Within the framework of this model and finite-difference parametric nonlinear equations of the reduced SIR (Susceptible-Infected-Removed) model, the fractal dimensions of various segments of daily incidence in the world and variations in the main reproduction number of COVID-19 were calculated based on the data of COVID-19 world statistics.

Comparative study of artificial neural network versus parametric method in COVID-19 data analysis

Since the previous two years, a new coronavirus (COVID-19) has found a major global problem. The speedy pathogen over the globe was followed by a shockingly large number of afflicted people and a gradual increase in the number of deaths. If the survival analysis of active individuals can be predicted, it will help to contain the epidemic significantly in any area. In medical diagnosis, prognosis and survival analysis, neural networks have been found to be as successful as general nonlinear models. In this study, a real application has been developed for estimating the COVID-19 mortality rates in Italy by using two different methods, artificial neural network modeling and maximum likelihood estimation. The predictions obtained from the multilayer artificial neural network model developed with 9 neurons in the hidden layer were compared with the numerical results. The maximum deviation calculated for the artificial neural network model was -0.14% and the R value was 0.99836. The study findings confirmed that the two different statistical models that were developed had high reliability.

A novel extended model with versatile shaped failure rate: Statistical inference with Covid -19 applications

Statistical models perform an essential role in data analysis, and statisticians are constantly looking for novel or pretty recent statistical models to fit data sets across a broad variety of fields. In this study, we used modified Kies generalized transformation and the new power function to suggest an unique statistical model. We present and discuss a linear illustration of the density function. Theoretically, quantile function, characteristic function, stochastic ordering, mean, and moments are just a few of the structure properties we discuss. By defining an ideal statistical distribution for assessing the COVID-19 mortality rate, an attempt is performed to determine the model of COVID-19 spread in different nations like the United Kingdom and Italy. In some countries, the novel distribution have been shown to be more appropriate than existing competing models when fitted to COVID-19.

Solution of a dynamical memory effect COVID-19 infection system with leaky vaccination efficacy by non-singular kernel fractional derivatives

In this paper, the recent trends of COVID-19 infection spread have been studied to explore the advantages of leaky vaccination dynamics in SEVR (Susceptible Effected Vaccinated Recovered) compartmental model with the help of Caputo-Fabrizio (CF) and Atangana-Baleanu derivative in the Caputo sense (ABC) non-singular kernel fractional derivative operators with memory effect within the model to show possible long-term approaches of the infection along with limited defensive vaccine efficacy that can be designed numerically over the closed interval ranging from 0 to 1. One of the main goals is to provide a stepping information about the usefulness of the aforementioned non-singular kernel fractional approaches for a lenient case as well as a critical case in COVID-19 infection spread. Another is to investigate the effect of death rate on state variables. The estimation of death rate for state variables with suitable vaccine efficacy has a significant role in the stability of state variables in terms of basic reproduction number that is derived using next generation matrix method, and order of the fractional derivative. For non-integral orders the pandemic modeling sense viz, CF and ABC, has been compared thoroughly. Graphical presentations together with numerical results have proposed that the methodology is powerful and accurate which can provide new speculations for COVID-19 dynamical systems.

Future implications of COVID-19 through Mathematical modeling

COVID-19 is a pandemic respiratory illness. The disease spreads from human to human and is caused by a novel coronavirus SARS-CoV-2. In this study, we formulate a mathematical model of COVID-19 and discuss the disease free state and endemic equilibrium of the model. Based on the sensitivity indexes of the parameters, control strategies are designed. The strategies reduce the densities of the infected classes but do not satisfy the criteria/threshold condition of the global stability of disease free equilibrium. On the other hand, the endemic equilibrium of the disease is globally asymptotically stable. Therefore it is concluded that the disease cannot be eradicated with present resources and the human population needs to learn how to live with corona. For validation of the results, numerical simulations are obtained using fourth order Runge-Kutta method.

A new lifetime family of distributions: Theoretical developments and analysis of COVID 19 data

In parametric statistical modeling and inference, it is critical to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets. Thus , this paper contributes to the subject by investigating a new flexible and versatile generalized family of distributions defined from the alliance of the families known as beta-G and Topp-Leone generated (TL-G), inspiring the name of BTL-G family. The characteristics of this new family are studied through analytical, graphical and numerical approaches. Statistical features of the family such as expansion of density function (pdf), cumulative function (cdf), moments (MOs), incomplete moments (IMOs), mean deviation (MDE), and entropy (ENT) are calculated. The model parameters' maximum likelihood estimates (MaxLEs) and Bayesian estimates (BEs) are provided. Symmetric and Asymmetric Bayesian Loss function have been discussed. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of genuine COVID 19 data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

Stochastic covid-19 model with fractional global and classical piecewise derivative

Several methodologies have been advocated in the last decades with the aim to better understand behaviours displayed by some real-world problems. Among which, stochastics modelling and fractional modelling, fuzzy and others. These methodologies have been suggested to threat specific problems; however, It have been noticed that some problems exhibit different patterns as time passes by. Randomness and nonlocality can be combined to depict complex real-world behaviours. It has been observed that, covid-19 virus spread does not follow a single pattern; sometimes we obtained stochastic behaviours, another nonlocal behaviour and others. In this paper, we shall consider a covid-19 model with fractional stochastic behaviours. More precisely a covid-19 model, where the model considers nonlocalities and randomness is suggested. Then a comprehensive analysis of the model is conducted. Numerical simulations and illustrations are done to show the efficiency of the model.