A New Extension of the Kumaraswamy Exponential Model with Modeling of Food Chain Data

Statistical models are useful in explaining and forecasting real-world occurrences. Various extended distributions have been widely employed for modeling data in a variety of fields throughout the last few decades. In this article we introduce a new extension of the Kumaraswamy exponential (KE) model called the Kavya–Manoharan KE (KMKE) distribution. Some statistical and computational features of the KMKE distribution including the quantile (QUA) function, moments (MOms), incomplete MOms (INMOms), conditional MOms (COMOms) and MOm generating functions are computed. Classical maximum likelihood and Bayesian estimation approaches are employed to estimate the parameters of the KMKE model. The simulation experiment examines the accuracy of the model parameters by employing Bayesian and maximum likelihood estimation methods. We utilize two real datasets related to food chain data in this work to demonstrate the importance and flexibility of the proposed model. The new KMKE proposed distribution is very flexible, more so than numerous well-known distributions.

Data analysis for COVID-19 deaths using a novel statistical model: Simulation and fuzzy application.

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.

On Unit Exponential Pareto Distribution for Modeling the Recovery Rate of COVID-19

In 2019, a new lethal and mutant virus (COVID-19) spread around the world, causing the deaths of millions of people. COVID-19 demonstrates that scientists are involved in significant research efforts to face bacteria with less effort than that dedicated to viruses. Since then, engineers and bio-materials scientists have been trying to develop antiviral research and find a suitable effective medication. Strategies and opportunities for interference diagnostics, treatment strategies, and predicting future factors became mandatory. From a statistical point of view, estimating and modelling these factors play an important role in preventing future viral epidemics. In this article, modelling the recovery rate of COVID-19 is investigated through a new distribution which is called the unit exponential Pareto distribution. The new continuous distribution with three parameters displays a prominent level of flexibility to model decreasing, symmetric, and asymmetric data with a monotone failure rate. The recovery rates of COVID-19 in Turkey and France were examined;moreover, milk production data and components' failure rates are presented for data modeling. The obtained results proved the superiority of the newly suggested model compared to other unit-based distributions. Several statistical features are studied such as the quantile function, the moments, the moment-generating function, some entropy measures, the ordered statistics, the stress-strength, and stochastic ordering. Two classical estimation methods are used in addition to the Bayesian method. The statistical features and estimation analysis are evaluated using numerical and simulation techniques. As a result, we obtain the efficiency of using the Bayesian method over the classical ones, with respect to the bias, average squared error, and the length of confidence intervals for the unknown parameters.

Weighted power Maxwell distribution: Statistical inference and COVID-19 applications.

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.

Optimal Analysis of Adaptive Type-II Progressive Censored for New Unit-Lindley Model

The parameters, reliability, and hazard rate functions of the Unit-Lindley distribution based on adaptive Type-II progressive censored sample are estimated using both non-Bayesian and Bayesian inference methods in this study. The Newton-Raphson method is used to obtain the maximum likelihood and maximum product of spacing estimators of unknown values in point estimation. On the basis of observable Fisher information data, estimated confidence ranges for unknown parameters and reliability characteristics are created using the delta approach and the frequentist estimators’ asymptotic normality approximation. To approximate confidence intervals, two bootstrap approaches are utilized. Using an independent gamma density prior, a Bayesian estimator for the squared-error loss is derived. The Metropolis-Hastings algorithm is proposed to approximate the Bayesian estimates and also to create the associated highest posterior density credible intervals. Extensive Monte Carlo simulation tests are carried out to evaluate the performance of the developed approaches. For selecting the optimum progressive censoring scheme, several optimality criteria are offered. A practical case based on COVID-19 data is used to demonstrate the applicability of the presented methodologies in real-life COVID-19 scenarios.

Bayesian and Non-Bayesian Inference for Unit-Exponentiated Half-Logistic Distribution with Data Analysis

Unit distributions are typically used in probability theory and statistics to illustrate useful quantities with values between zero and one. In this paper, we investigated an appropriate transformation to propose the unit-exponentiated half-logistic distribution (UEHLD), which is also beneficial for modelling data on the unit interval. This distribution's mathematical features are supplied, including moments, probability-weighted moments, incomplete moments, various entropy measures, and stress–strength reliability. Using well-known estimation techniques such as the maximum likelihood, maximum product of spacing, and Bayesian inference, the estimators of the parameters relevant to the proposed distribution were determined. A comprehensive simulation analysis is provided to examine the performance of parameter estimation approaches on finite samples. The proposed distribution was realistically applied to data on economic growth and data on the tensile strength of polyester fibers to provide an explanation. Furthermore, the analysis of COVID-19 data from Britain as a medical statistical dataset is provided. The experimental results demonstrate that the suggested UEHLD yields a better comparison with some new unit distributions, as well as other unbounded distributions.

Modeling of COVID-19 vaccination rate using odd Lomax inverted Nadarajah-Haghighi distribution.

Since the spread of COVID-19 pandemic in early 2020, modeling the related factors became mandatory, requiring new families of statistical distributions to be formulated. In the present paper we are interested in modeling the vaccination rate in some African countries. The recorded data in these countries show less vaccination rate, which will affect the spread of new active cases and will increase the mortality rate. A new extension of the inverted Nadarajah-Haghighi distribution is considered, which has four parameters and is obtained by combining the inverted Nadarajah-Haghighi distribution and the odd Lomax-G family. The proposed distribution is called the odd Lomax inverted Nadarajah-Haghighi (OLINH) distribution. This distribution owns many virtuous characteristics and attractive statistical properties, such as, the simple linear representation of density function, the flexibility of the hazard rate curve and the odd ratio of failure, in addition to other properties related to quantile, the rth-moment, moment generating function, Rényi entropy, and the function of ordered statistics. In this paper we address the problem of parameter estimation from frequentest and Bayesian approach, accordingly a comparison between the performance of the two estimation methods is implemented using simulation analysis and some numerical techniques. Finally different goodness of fit measures are used for modeling the COVID-19 vaccination rate, which proves the suitability of the OLINH distribution over other competitive distributions.

An Overview of Discrete Distributions in Modelling COVID-19 Data Sets.

The mathematical modeling of the coronavirus disease-19 (COVID-19) pandemic has been attempted by a large number of researchers from the very beginning of cases worldwide. The purpose of this research work is to find and classify the modelling of COVID-19 data by determining the optimal statistical modelling to evaluate the regular count of new COVID-19 fatalities, thus requiring discrete distributions. Some discrete models are checked and reviewed, such as Binomial, Poisson, Hypergeometric, discrete negative binomial, beta-binomial, Skellam, beta negative binomial, Burr, discrete Lindley, discrete alpha power inverse Lomax, discrete generalized exponential, discrete Marshall-Olkin Generalized exponential, discrete Gompertz-G-exponential, discrete Weibull, discrete inverse Weibull, exponentiated discrete Weibull, discrete Rayleigh, and new discrete Lindley. The probability mass function and the hazard rate function are addressed. Discrete models are discussed based on the maximum likelihood estimates for the parameters. A numerical analysis uses the regular count of new casualties in the countries of Angola,Ethiopia, French Guiana, El Salvador, Estonia, and Greece. The empirical findings are interpreted in-depth.

Novel Type I Half Logistic Burr-Weibull Distribution: Application to COVID-19 Data.

In this work, we presented the type I half logistic Burr-Weibull distribution, which is a unique continuous distribution. It offers several superior benefits in fitting various sorts of data. Estimates of the model parameters based on classical and nonclassical approaches are offered. Also, the Bayesian estimates of the model parameters were examined. The Bayesian estimate method employs the Monte Carlo Markov chain approach for the posterior function since the posterior function came from an uncertain distribution. The use of Monte Carlo simulation is to assess the parameters. We established the superiority of the proposed distribution by utilising real COVID-19 data from varied countries such as Saudi Arabia and Italy to highlight the relevance and flexibility of the provided technique. We proved our superiority using both real data.

The Power XLindley Distribution: Statistical Inference, Fuzzy Reliability, and COVID-19 Application

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. [ FROM AUTHOR] Copyright of Journal of Function Spaces is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data

The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), residual life and reversed residual life functions, and entropy. The maximum likelihood (ML) and Bayesian estimations are developed based on the Type-II censored sample. The properties of Bayes estimators of the parameters are studied under different loss functions (squared error loss function and LINEX loss function). To create Markov-chain Monte Carlo samples from the posterior density, the Metropolis–Hasting technique was used with posterior density. Using non-informative and informative priors, a full simulation technique was carried out. The maximum likelihood estimator was compared to the Bayesian estimators using Monte Carlo simulation. To compare the performances of the suggested estimators, a simulation study was carried out. Real-world data sets, such as strength measured in GPA for single carbon fibers and impregnated 1000-carbon fiber tows, maximum stress per cycle at 31,000 psi, and COVID-19 data were used to demonstrate the relevance and flexibility of the suggested method. The suggested models are then compared to comparable models such as the Marshall–Olkin alpha power exponential, the extended odd Weibull exponential, the Weibull–Rayleigh, the Weibull–Lomax, and the exponential Lomax distributions.

BAYESIAN INFERENCE FOR THE PARAMETERS OF EXPONENTIATED CHEN DISTRIBUTION BASED ON HYBRID CENSORING

This article presents classical and Bayesian inferences based on Type-II hybrid censored data when the lifetime of the items follows the exponentiated Chen distribution. Based on the hybrid censored data, the maximum likelihood estimates and the asymptotic confidence intervals of the involved parameters are derived. Bayes estimates, under squared error loss and linear-exponential loss functions, and highest posterior density intervals are also derived. Monte Carlo simulations are performed to see the effectiveness of the proposed estimation methods. The Application of real data from Vaccination of COVID-19 data for different countries of the region of the Americas is discussed. [ FROM AUTHOR] Copyright of Pakistan Journal of Statistics is the property of Pakistan Journal of Statistics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

A superior extension for the Lomax distribution with application to Covid-19 infections real data

We present a new continuous lifetime model with four parameters by combining the Lomax and the Weibull distributions. The extended odd Weibull Lomax (EOWL) distribution is what we’ll call it. This new distribution possesses several desirable properties thanks to the simple linear representation of its hazard rate function, moments, and moment -generating function, with stress-strength reliability that are provided in a simple closed forms. The parameters of the EOWL model are estimated using classical methods such as the maximum likelihood (MLE) and the maximum product of spacing (MPS) and estimated also but using a non-classical method such as Bayesian analytical approaches. Bayesian estimation is performed using the Monte Carlo Markov Chain method. Monte Carlo simulation are used to assess the effectiveness of the estimation methods throughout the Metropolis Hasting (MH) algorithm. To illustrate the suggested distribution’s effectiveness and suitability for simulating real-world pandemics, we used three existing COVID-19 data sets from the United Kingdom, the United States of America, and Italy which are studied to serve as illustrative examples. We graphed the P-P plots and TTT plots for the proposed distribution proving its superiority in a graphical manner for modelling the three data sets in the paper.

The New Novel Discrete Distribution with Application on COVID-19 Mortality Numbers in Kingdom of Saudi Arabia and Latvia

This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.

The new discrete distribution with application to COVID-19 Data.

This research aims to model the COVID-19 in different countries, including Italy, Puerto Rico, and Singapore. Due to the great applicability of the discrete distributions in analyzing count data, we model a new novel discrete distribution by using the survival discretization method. Because of importance Marshall-Olkin family and the inverse Toppe-Leone distribution, both of them were used to introduce a new discrete distribution called Marshall-Olkin inverse Toppe-Leone distribution, this new distribution namely the new discrete distribution called discrete Marshall-Olkin Inverse Toppe-Leone (DMOITL). This new model possesses only two parameters, also many properties have been obtained such as reliability measures and moment functions. The classical method as likelihood method and Bayesian estimation methods are applied to estimate the unknown parameters of DMOITL distributions. The Monte-Carlo simulation procedure is carried out to compare the maximum likelihood and Bayesian estimation methods. The highest posterior density (HPD) confidence intervals are used to discuss credible confidence intervals of parameters of new discrete distribution for the results of the Markov Chain Monte Carlo technique (MCMC).

Type I Half Logistic Burr X-G Family: Properties, Bayesian, and Non-Bayesian Estimation under Censored Samples and Applications to COVID-19 Data

In this paper, we present a new family of continuous distributions known as the type I half logistic Burr X-G. The proposed family's essential mathematical properties, such as quantile function (QuFu), moments (Mo), incomplete moments (InMo), mean deviation (MeD), Lorenz (Lo) and Bonferroni (Bo) curves, and entropy (En), are provided. Special models of the family are presented, including type I half logistic Burr X-Lomax, type I half logistic Burr X-Rayleigh, and type I half logistic Burr X-exponential. The maximum likelihood (MLL) and Bayesian techniques are utilized to produce parameter estimators for the recommended family using type II censored data. Monte Carlo simulation is used to evaluate the accuracy of estimates for one of the family's special models. The COVID-19 real datasets from Italy, Canada, and Belgium are analysed to demonstrate the significance and flexibility of some new distributions from the family. [ABSTRACT FROM AUTHOR] Copyright of Mathematical Problems in Engineering is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A New Transmuted Generalized Lomax Distribution: Properties and Applications to COVID-19 Data.

A new five-parameter transmuted generalization of the Lomax distribution (TGL) is introduced in this study which is more flexible than current distributions and has become the latest distribution theory trend. Transmuted generalization of Lomax distribution is the name given to the new model. This model includes some previously unknown distributions. The proposed distribution's structural features, closed forms for an rth moment and incomplete moments, quantile, and Rényi entropy, among other things, are deduced. Maximum likelihood estimate based on complete and Type-II censored data is used to derive the new distribution's parameter estimators. The percentile bootstrap and bootstrap-t confidence intervals for unknown parameters are introduced. Monte Carlo simulation research is discussed in order to estimate the characteristics of the proposed distribution using point and interval estimation. Other competitive models are compared to a novel TGL. The utility of the new model is demonstrated using two COVID-19 real-world data sets from France and the United Kingdom.

Kumaraswamy Inverted Topp–Leone Distribution with Applications to COVID-19 Data

In this paper, an attempt is made to discover the distribution of COVID-19 spread in different countries such as;Saudi Arabia, Italy, Argentina and Angola by specifying an optimal statistical distribution for analyzing the mortality rate of COVID-19. A new generalization of the recently inverted Topp Leone distribution, called Kumaraswamy inverted Topp–Leone distribution, is proposed by combining the Kumaraswamy-G family and the inverted Topp–Leone distribution. We initially provide a linear representation of its density function. We give some of its structure properties, such as quantile function, median, moments, incomplete moments, Lorenz and Bonferroni curves, entropies measures and stress-strength reliability. Then, Bayesian and maximum likelihood estimators for parameters of the Kumaraswamy inverted Topp–Leone distribution under Type-II censored sample are considered. Bayesian estimator is regarded using symmetric and asymmetric loss functions. As analytical solution is too hard, behaviours of estimates have been done viz Monte Carlo simulation study and some reasonable comparisons have been presented. The outcomes of the simulation study confirmed the efficiencies of obtained estimates as well as yielded the superiority of Bayesian estimate under adequate priors compared to the maximum likelihood estimate. Application to COVID-19 in some countries showed that the new distribution is more appropriate than some other competitive models.

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.