The Topp-Leone Extended Exponential Distribution: Estimation Methods and Applications

Al-Shomrani et al. (2016) introduced a new family of distributions (TL-G) based on the Topp-Leone distribution (TL) by replacing the variable x by any cumulative distribution function G(t). With only one extra parameter which controls the skewness, this family is a good competitor to several generalized distributions used in statistical analysis. In this work, we consider the extended exponential as the baseline distribution G to obtain a new model called the Topp-Leone extended exponential distribution TL-EE. After studying mathematical and statistical properties of this model, we propose different estimation methods such as maximum likelihood estimation, method of ordinary and weighted least squares, method of percentile, method of maximum product of spacing, method of Cramer Von-Mises, modified least squares estimators and chi-square minimum method for estimating the unknown parameters. In addition to the classical criteria for model selection, we develop for this distribution a goodness-of-fit statistic test based on a modification of Pearson statistic. The performances of the methods used are demonstrated by an extensive simulation study. With applications to covid-19 data and waiting times for bank service, a comparison evaluation shows that the proposed model describes data better than several competing distributions.

The Maxwell-Burr X Distribution: Its Properties and Applications to the COVID-19 Mortality Rate in Thailand

A novel distribution, the Maxwell-Burr X (M-BX) distribution, was proposed. This distribution was an extension of the Burr X distribution by applying the Maxwell generalized family of distributions. The cumulative distribution function, probability density function, survival function, hazard function and quantile function of the M-BX distribution were defined. Some important properties and the parameters of its estimates were discussed. A simulation study was conducted from the basis of quantile function to ascertain the performance of maximum likelihood estimators. The M-BX distribution were also applied to model two lifetime data sets relating to the COVID-19 mortality rate in Thailand during different periods to express the flexibility of the distribution against other competing distributions. According to information criteria, AIC, CAIC, BIC, and HQIC, the M-BX distribution gave the best fit among all chosen distributions. © 2023, Thai Statistical Association. All rights reserved.

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.

Truncated Rayleigh Odd Weibull Exponential Distribution with Application to COVID-19 Data

A proposed truncated Rayleigh odd Weibull-G family with one ofits sub-models, truncated Rayleigh odd Weibull exponential distribution, are introduced. Several statistical properties along with linear representation, reliability measures, entropies, and reliability stress strength model are presented. The unknown parameters are estimated through the maximum likelihood method. Simulation and real application are used to evaluate the new distribution's flexibility and usefulness. For different compared information criteria, the results clearly show that the proposed distribution has superior output relative to other competitive distributions demonstrating its consistent and flexible performance, as well as representing an optimal statistical model for the distribution of COVID-19 death cases in Iraq. © 2022 IEEE.

A new generalization of Nadarajah-Haghighi distribution with application to cancer and COVID-19 deaths data

In this article, a new flexible distribution called shifted generalized truncated Nadarajah-Haghighi (SGeTNH) distribution is generalized from the Nadarajah-Haghighi distribution. The hazard rate function of SGeTNH distribution is very flexible and can be increasing, decreasing, bathtub-shaped, upside-down bathtub-shaped, depending on the parameter values. Estimations of parameters of the proposed distribution are derived based on the alternative maximum likelihood estimation (AMLE), least squares estimation (LSE), and Cramér-von Mises estimation (CVME) methods. Monte Carlo simulations are performed to show the accuracy of the proposed methods of estimations. Several real data sets on cancer deaths and COVID-19 daily mortality are applied to illustrate the flexibility and usefulness of SGeTNH distribution for modeling reliability data.

Association of statin use with outcomes of patients admitted with COVID-19: an analysis of electronic health records using superlearner.

IMPORTANCE: Statin use prior to hospitalization for Coronavirus Disease 2019 (COVID-19) is hypothesized to improve inpatient outcomes including mortality, but prior findings from large observational studies have been inconsistent, due in part to confounding. Recent advances in statistics, including incorporation of machine learning techniques into augmented inverse probability weighting with targeted maximum likelihood estimation, address baseline covariate imbalance while maximizing statistical efficiency. OBJECTIVE: To estimate the association of antecedent statin use with progression to severe inpatient outcomes among patients admitted for COVD-19. DESIGN, SETTING AND PARTICIPANTS: We retrospectively analyzed electronic health records (EHR) from individuals ≥ 40-years-old who were admitted between March 2020 and September 2022 for ≥ 24 h and tested positive for SARS-CoV-2 infection in the 30 days before to 7 days after admission. EXPOSURE: Antecedent statin use-statin prescription ≥ 30 days prior to COVID-19 admission. MAIN OUTCOME: Composite end point of in-hospital death, intubation, and intensive care unit (ICU) admission. RESULTS: Of 15,524 eligible COVID-19 patients, 4412 (20%) were antecedent statin users. Compared with non-users, statin users were older (72.9 (SD: 12.6) versus 65.6 (SD: 14.5) years) and more likely to be male (54% vs. 51%), White (76% vs. 71%), and have ≥ 1 medical comorbidity (99% vs. 86%). Unadjusted analysis demonstrated that a lower proportion of antecedent users experienced the composite outcome (14.8% vs 19.3%), ICU admission (13.9% vs 18.3%), intubation (5.1% vs 8.3%) and inpatient deaths (4.4% vs 5.2%) compared with non-users. Risk differences adjusted for labs and demographics were estimated using augmented inverse probability weighting with targeted maximum likelihood estimation using Super Learner. Statin users still had lower rates of the composite outcome (adjusted risk difference: - 3.4%; 95% CI: - 4.6% to - 2.1%), ICU admissions (- 3.3%; - 4.5% to - 2.1%), and intubation (- 1.9%; - 2.8% to - 1.0%) but comparable inpatient deaths (0.6%; - 1.3% to 0.1%). CONCLUSIONS AND RELEVANCE: After controlling for confounding using doubly robust methods, antecedent statin use was associated with minimally lower risk of severe COVID-19-related outcomes, ICU admission and intubation, however, we were not able to corroborate a statin-associated mortality benefit.

A new multivariate transmuted family of distributions: theory and application for modelling of daily world COVID-19 cases

Multivariate distributions are helpful in the simultaneous modeling of several dependent random variables. The development of a unique multivariate distribution has been a difficult task and different multivariate versions of the same distribution are available. The need is, therefore, to suggest a method of obtaining a multivariate distribution from the univariate marginals. In this paper, we have proposed a new method of generating the multivariate families of distributions when information on univariate marginals is available. Specifically, we have proposed a multivariate family of distributions which provides a univariate transmuted family of distributions as marginal. The proposed family is a re-parameterization of the Cambanis (1977) family. Some properties of the proposed family of distributions have been studied. These properties include marginal and joint marginal distributions, conditional distributions, and marginal and conditional moments. We have also obtained the dependence measures alongside the maximum likelihood estimation of the parameters. The proposed multivariate family of distributions is studied for the Weibull baseline distributions giving rise to the multivariate transmuted Weibull (MTW) distribution. Real data application of the proposed MTW distribution is given in the context of modeling the daily COVID-19 cases of the World. It is observed that the proposed MTW distribution is a suitable fit for the joint modeling of the COVID-19 data. © 2022, National Science Foundation. All rights reserved.

A New Extension of the Topp–Leone-Family of Models with Applications to Real Data

In this article, we proposed a new extension of the Topp–Leone family of distributions. Some important properties of the model are developed, such as quantile function, stochastic ordering, model series representation, moments, stress–strength reliability parameter, Renyi entropy, order statistics, and moment of residual life. A particular member called new extended Topp–Leone exponential (NETLE) is discussed. Maximum likelihood estimation (MLE), least-square estimation (LSE), and percentile estimation (PE) are used for the model parameter estimation. Simulation studies were conducted using NETLE to assess the MLE, LSE, and PE performance by examining their bias and mean square error (MSE), and the result was satisfactory. Finally, the applications of the NETLE to two real data sets are provided to illustrate the importance of the NETLG families in practice;the data sets consist of daily new deaths due to COVID-19 in California and New Jersey, USA. The new model outperformed many other existing Topp–Leone's and exponential related distributions based on the real data illustrations.

Reconstruction of Human Trajectories Based on Anonymous Sensor Data for Estimating Infection Route

The COVID-19 Pandemic has increased the demands of governments for technologies to estimate the route of infection. In this paper, we propose a new smart city framework that collects anonymized passage information from deployed Bluetooth sensors and analyzes them to reconstruct the multiple trajectories of infected people. We formulate recovering multiple trajectories on the basis of anonymized passage information, including passage time and passage position, obtained by sensors in a smart city as a problem of multiple-trajectory reconstruction in general networks. We propose a new method for reconstructing multiple trajectories on the basis of anonymized passage information. Our method assumes that each trajectory follows a Markov process and estimates transit time for each edge in networks and the transition probability of the Markov process. On the basis of its estimation, our method can find multiple trajectories with maximum likelihood by solving a minimum cost flow problem. We evaluate the performance of our method in experiments using simulation data and actual human trajectory data. © 2022 IEEE.

A Demonstration of Modified Treatment Policies to Evaluate Shifts in Mobility and COVID-19 Case Rates in US Counties.

Mixed evidence exists of associations between mobility data and coronavirus disease 2019 (COVID-19) case rates. We aimed to evaluate the county-level impact of reducing mobility on new COVID-19 cases in summer/fall of 2020 in the United States and to demonstrate modified treatment policies to define causal effects with continuous exposures. Specifically, we investigated the impact of shifting the distribution of 10 mobility indexes on the number of newly reported cases per 100,000 residents 2 weeks ahead. Primary analyses used targeted minimum loss-based estimation with Super Learner to avoid parametric modeling assumptions during statistical estimation and flexibly adjust for a wide range of confounders, including recent case rates. We also implemented unadjusted analyses. For most weeks, unadjusted analyses suggested strong associations between mobility indexes and subsequent new case rates. However, after confounder adjustment, none of the indexes showed consistent associations under mobility reduction. Our analysis demonstrates the utility of this novel distribution-shift approach to defining and estimating causal effects with continuous exposures in epidemiology and public health.

Generalization of the Lindley distribution with application to COVID-19 data.

Creating new distributions with more desired and flexible qualities for modeling lifetime data has resulted in a concentrated effort to modify or generalize existing distributions. In this paper, we propose a new distribution called the power exponentiated Lindley (PEL) distribution by generalizing the Lindley distribution using the power exponentiated family of distributions, that can fit lifetime data. Then the main statistical properties such as survival function, hazard function, reverse hazard function, moments, quantile function, stochastic ordering, MRL, order statistics, etc., of the newly proposed distribution have been derived. The parameters of the distribution are estimated using the MLE method. Then, a Monte Carlo simulation study is used to check the consistency of the parameters of the PEL distribution in terms of MSE, RMSE, and bias. Finally, we implement the PEL distribution as a statistical lifetime model for the COVID-19 case fatality ratio (in %) in China and India, and the new cases of COVID-19 reported in Delhi. Then we check whether the new distribution fits the data sets better than existing well-known distributions. Different statistical measures such as the value of the log-likelihood function, K-S statistic, AIC, BIC, HQIC, and p-value are used to assess the accuracy of the model. 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.

An extended approach for the generalized powered uniform distribution.

A new uniform distribution model, generalized powered uniform distribution (GPUD), which is based on incorporating the parameter k into the probability density function (pdf) associated with the power of random variable values and includes a powered mean operator, is introduced in this paper. From this new model, the shape properties of the pdf as well as the higher-order moments, the moment generating function, the model that simulates the GPUD and other important statistics can be derived. This approach allows the generalization of the distribution presented by Jayakumar and Sankaran (2016) through the new GPUD ( J - S ) distribution. Two sets of real data related to COVID-19 and bladder cancer were tested to demonstrate the proposed model's potential. The maximum likelihood method was used to calculate the parameter estimators by applying the maxLik package in R. The results showed that this new model is more flexible and useful than other comparable models.

Comparison of the Effective Reproduction Number (Rt) Estimation Methods of COVID-19 Using Simulation Data Based on Available Data from Iran, USA, UK, India, and Brazil.

BACKGROUND: Accurate determination of the effective reproduction number (Rt) is a very important strategy in the epidemiology of contagious diseases, including coronavirus disease 2019 (COVID-19). This study compares different methods of estimating the Rt of susceptible population to identify the most accurate method for estimating Rt. STUDY DESIGN: A secondary study. METHODS: The value of Rt was estimated using attack rate (AR), exponential growth (EG), maximum likelihood (ML), time-dependent (TD), and sequential Bayesian (SB) methods, for Iran, the United States, the United Kingdom, India, and Brazil from June to October 2021. In order to accurately compare these methods, a simulation study was designed using forty scenarios. RESULTS: The lowest mean square error (MSE) was observed for TD and ML methods, with 15 and 12 cases, respectively. Therefore, considering the estimated values of Rt based on the TD method, it was found that Rt values in the United Kingdom (1.33; 95% CI: 1.14-1.52) and the United States (1.25; 95% CI: 1.12-1.38) substantially have been more than those in other countries, such as Iran (1.07; 95% CI: 0.95-1.19), India (0.99; 95% CI: 0.89-1.08), and Brazil (0.98; 95% CI: 0.84-1.14) from June to October 2021. CONCLUSION: The important result of this study is that TD and ML methods lead to a more accurate estimation of Rt of population than other methods. Therefore, in order to monitor and determine the epidemic situation and have a more accurate prediction of the incidence rate, as well as control COVID-19 and similar diseases, the use of these two methods is suggested to more accurately estimate Rt.

Satellite Data Investigation for Change Estimation During COVID Era by Fusing Pixel and Object-Based Technique

In this investigation, an innovative combination of pixel-based change detection technique and object-based change detection technique is explored with the satellite images of Holy Masjid al-Haram, Saudi Arabia. The gray-level co-occurrence matrix (GLCM) method is used to quantify the texture of the remote sensing data through the texture classification approach on the satellite data in this work. GLCM produces results of the texture quantification in normalized form. Thus, applying a texture classification scheme on the satellite data is impressive to observe. Later maximum likelihood image classification approach is used for classification purposes. The classified information is categorized into four different classes. The kappa coefficient’s value and the overall accuracy for the pre- COVID classified study area are 0.6532 and 76.38%, respectively. During COVID, the classified study area presents the kappa coefficient and the overall accuracy of 0.7631 and 82.18%, respectively. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Quantifying the Effects of Non-Pharmaceutical and Pharmaceutical Interventions Against Covid-19 Epidemic in the Republic of Korea: Mathematical Model-Based Approach Considering Age Groups and the Delta Variant

Early vaccination efforts and non-pharmaceutical interventions (NPIs) were insufficient to prevent a surge of COVID-19 cases triggered by the Delta variant. A compartment model that includes age, vaccination, and variants was developed. We estimated the transmission rates using maximum likelihood estimation, and phase-dependent NPIs according to government policies from 26 February to 8 October 2021. Simulations were done to examine the effects of varying dates of initiation and intensity of eased NPIs, arrival timing of Delta, and speed of vaccine administration. The estimated transmission rate matrices show distinct patterns, with transmission rates of younger groups (0-39 years) much larger with Delta. Social distancing (SD) level 2 and SD4 in Korea were associated with transmission reduction factors of 0.63-0.70 and 0.70-0.78, respectively. The easing of NPIs to a level comparable to SD2 should be initiated not earlier than 16 October to keep the number of severe cases below Korea's healthcare capacity. Simulations showed that a surge prompted by Delta can be prevented if the number of people vaccinated daily or SD level when Delta arrived was higher. The timing of easing, intensity of NPIs, vaccination speed, and screening measures are key factors in preventing another epidemic wave.

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.

A Non-autonom SIR Model in Epidemiology

With the outbreak of COVID-19, the modelling of epidemic spread has once again become highly important. This paper introduces an epidemic spreading model with a changing infection rate. This model extends the traditional SIR (Susceptible – Infected – Removed) model. The SIR model is a dynamic model which divides individuals into 3 groups: susceptible, infected, and removed (including recovered and died). Individuals in each group have a constant proportion to change to the next group. This paper assumes the infection rate is dependent on the development cycle of the virus, which can vary in the different periods since being infected, instead of constants. This makes the differential equations a non-autonomous model. This paper works on how to fit the function of the infection rate and solve the equations. This paper uses Burr distribution which has 3 unknown parameters as the function of infection rate, and then discusses about two different methods to get these parameters—the least-squares method and the maximum likelihood estimation. As a numerical experiment of this model, this paper uses the data of COVID-19 in Ireland to make predictions and compare with the traditional SIR model. The non-autonomous model in this paper shows better performance than the traditionary SIR model. This new model might be potential in further epidemic simulation, and it is not hard to be combined with other extensions of the SIR model. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Probability Distributions for Modeling of COVID-19 cases and deaths in Thailand

The COVID-19 is a pandemic and continues to mutate and spread within Thailand and throughout the world. Recently, Omicron is a new COVID-19 variant of concern because it has several mutations that may have an impact on how it behaves. It is therefore important to understand COVID-19 dynamics in order to prevent or control infections appropriately. In this study, we analyzed a model of the daily number of COVID-19 cases and deaths in Thailand using five different probability distributions. Maximum likelihood estimation (MLE) is applied to estimate parameters of the five distributions. The results indicate that the Weibull distribution and the log-normal distribution are the most suitable distributions that fit the data on daily confirmed cases and on daily confirmed deaths, respectively, by using the Akaike information criterion (AIC) and the Bayes information criterion (BIC). © 2022. International Journal of Mathematics and Computer Science. All Rights Reserved.

A new unit distribution: Properties, inference, and applications

We propose a new bounded distribution called the Marshall–Olkin reduced- Kies distribution, which is a competitive model to the generalized beta, Kumaraswamy and beta distributions. It is able to model both negative and positive skewed data. Eight classical estimation methods are used to estimate its parameters. A simulation study is conducted to compare the performance of the different estimators. The performance ordering of these estimators is explored using partial and overall ranks to determine the best estimation method. Two COVID-19 data sets on to recovering and death rates in Spain are analyzed to show the flexibility of the new distribution to model such data. The expected values of the first and last order statistics are used to estimate the minimum and maximum recovery and death rates. © 2022

Estimation of Basic Reproduction Number and Herd Immunity for COVID-19 in India

In recent times, the rapid rise of the COVID-19 has imparted a devastating effect on human society. India has been perceiving the significant impacts of the COVID-19 in many ways. Estimation of basic reproduction number and herd immunity has become an important question which might support policy makers to take decisions for the improvement of the current scenario. In this chapter, the autoregressive integrated moving average (ARIMA) tool has been used to estimate confirm cases, discharge, deaths, and case fatality rate due to COVID-19 in India during March 1st–May 6th, 2020. The sequential bayesian (SB) method, Wallinga and Teunis approach (TD), exponential growth (EG), and maximum likelihood (ML) techniques are used to estimate the basic reproduction number and herd immunity due to COVID-19 in India. The findings are: basic reproduction number in earlier method as follows, 1.6998 (95% CI, 1.4595–1.9210), 1.8043 (95% CI, 1.6287–1.9894), 1.4685 (95% CI, 1.4672–1.4698) and 1.8931 (95% CI, 1.8655–1.9210) in SB, TD, EG, and ML, respectively. The estimations of herd immunity as follows for SB, TD, EG, and ML such as, 0.4116 (95% CI, 0.3148–0.4794), 0.4457 (95% CI, 0.3860–0.4973), 0.3190 (95% CI, 0.3184–0.3196), and 0.4717 (95% CI, 0.4639–0.4794), respectively. Results demonstrate the significant impact of epidemic dynamics of COVID-19 in India. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.