European Journal of Statistics

An Effective Method for Estimating the Population Mean That Utilizes Dual Auxiliary Information

Muhammad Asim Masood — 2024-11-18

To improve the effectiveness of population estimators, researchers have recently implemented dual supplementary information. They employed traditional rankings, the empirical cumulative distribution function, and indicator functions as supplementary sources of information in their analysis. An improved family of population mean estimators is introduced in this article, which utilizes the relative ranks of the auxiliary information’s configurations to incorporate the relevant information. A first-order approximation is employed to derive the mathematical expressions for the bias and the mean-squared error (MSE) of the proposed family of estimators. The empirical analysis is investigated to demonstrate the practicality of the proposed estimators in real-world scenarios. Additionally, the theoretical conclusions are effectively validated by the Monte Carlo simulation integration. Our results unequivocally indicate that the proposed family of estimators surpasses their current counterparts.

Generalized Arctan-Laplace Distribution: Properties and Applications

Ievgen Turchyn — 2024-11-07

A new asymmetric counterpart of the Laplace distribution is introduced, the Arctan-Laplace distribution. Its mathematical properties are studied. Flexibility of the proposed distribution family is demonstrated using a real data set.

Modeling and Prediction of Exchange Rates Using Topp-Leone Burr Type X, Machine Learning and Deep Learning Models

Hanita Daud — 2024-11-07

This paper introduces the Topp-Leone Burr X distribution (TLBXD), a novel extension of the Burr X distribution, developed within the framework of the Topp-Leone-G family. The TLBXD is designed to effectively model varying datasets, addressing the limitations of classical distributions when applied to heterogeneous data. We derived and presented key mathematical and statistical properties of the TLBXD, ensuring their clarity and applicability for practical use. A simulation study was conducted to evaluate the efficiency of different parameter estimation methods, including least squares (LS), maximum product of spacings (MPS), weighted least squares (WLS), and maximum likelihood (ML). The proposed distribution was applied to two real-world dates related to the daily exchange rates of the Nigerian Naira against the EURO and RIYAL. The TLBXD demonstrated superior performance compared to existing sub-models. In addition to the data modeling, this research also applied the proposed distribution to explore the predictive capabilities of machine learning and deep learning techniques for exchange rate forecasting. Three machine learning models, including the Extreme Gradient Boosting (XGBoost), Random Forest, and Light Gradient Boosting Machine (LightGBM) were evaluated alongside a deep learning algorithm, the Long Short-Term Memory (LSTM). The models were trained on 80% of the data set and tested on the remaining 20% to assess prediction accuracy. The results reveal that the LSTM model has significantly outperformed the machine learning models in forecasting exchange rates, as evidenced by lower root means squared errors (RMSE) and mean absolute errors (MAE) values.

A New Survival Regression Model with Application to HIV Data

Jamilu Yunusa Falgore — 2024-11-07

Many studies are being conducted in the modern world to extend the life expectancy of people suffering from a range of illnesses, including fatal conditions like cancer and HIV/AIDS. Many patients are therefore anticipated to be permanently cured or cured for some time. A new survival regression model was proposed to study HIV data. An advantage of the new distribution is that it outperforms some of the existing distributions in the lifetime literature. We obtain the estimates of the parameters of the proposed model using the method of maximum likelihood. The survival regression model was fitted to a data set of 100 observations. Additionally, Cox-Snell residual analysis was considered. The proposed model proved its significance by fitting the HIV data well compared to other models. The proposed model can be recommended to fit data of this kind.

Proposal of a Modified Clayton Copula: Theory, Properties and Examples

Christophe Chesneau — 2024-09-24

The Clayton copula is a mathematical tool used in copula theory to model dependence between random variables. It is a notable member of the Archimedean copula family and is best known for its ability to capture tail dependence. In this article, we present a new modified variant of the Clayton copula that aims to improve its flexibility. The proposed modification scheme perturbs its Archimedean nature by integrating a bivariate product of logarithmic functions and an additional tuning parameter. The elaborated copula benefits from a more nuanced representation of the copula density, and negative dependence can be obtained in a regular manner. We study its properties, including limit results showing some connection with the Gumbel-Barnett copula, important related functions, modifications and extensions, simulation of random couples of values, various lower and upper bounds, various tail dependences, and the correlation properties through the medial correlation and the Kendall tau. As an example of probability application, a new modified bivariate Gaussian distribution is presented via equations and graphics. Finally, two special cases of copula are discussed, including a simple single-parameter copula, which is intended to be a practical alternative to the Clayton copula. A brief analysis on simulated data shows that it may be preferable to the Clayton copula according to the Akaike information criterion. The overall result contributes to the advancement of the theoretical foundations of copula-based modeling techniques.

A New Family of Distributions Based on Amalgamation of Two Methods with an Application to the Rayleigh Model

A. Abdulkadir — 2024-08-21

In this paper, we present the Alpha power generalized odd generalized exponential-G (APGOGE-G) family of distributions and provides the most common shapes of the hazard rate function: increasing, decreasing, bathtub, and inverted bathtub. We provide some of its structural properties. We estimate the parameters by maximum likelihood estimation method, and perform a simulation study to verify the asymptotic properties of the estimator for the inverse Weibull baseline. The practicality of the new APGOGE-Rayleigh model is shown through application to uncensored real dataset.

Measuring Asymmetric Tails Under Copula Distributions

Paramahnasa Pramanik — 2024-06-03

Extensive evidence has been gathered showcasing the prevalence of heavy-tailed distributions and asymmetric tail interdependence within equity and foreign exchange markets, particularly during times of crisis. Tail interdependence in financial markets often manifests as financial contagion, characterized by periods where declining prices and heightened volatility propagate across economic and financial sectors. This phenomenon causes markets that typically exhibit minimal or no correlation to behave similarly, often in opposition to fundamental principles. Instances of unwarranted contagion present a perplexing challenge, suggesting irrationality among market participants and defying conventional risk management strategies and optimal portfolio selections. Our objective is to construct a comprehensive framework for dissecting such occurrences, utilizing a metric of tail-nonexchangeable dependencies employing various copulas with diverse marginal distributions. We offer analytical insights into our measurement of tail order dependence to aid in understanding these events.

Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs

Jaya P. N. Bishwal — 2024-04-01

We study the quasi-likelihood and quasi Bayes estimator of the drift parameter in the stochastic partial differential equations when the process is observed at the arrival times of a Poisson process. Unlike the previous work, no commutativity condition is assumed between the operators in the equation. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the quasi-likelihood to estimate the drift parameter. Under certain non-degeneracy assumptions on the operators, we obtain the consistency and the asymptotic normality of the estimators.

New Sine Inverted Exponential Distribution: Properties, Simulation and Application

I. J. David — 2024-04-01

The New Sine Inverted Exponential Distribution, a new distribution model with just one parameter, is suggested in this study. The suggested model has several statistical qualities and reliability properties that have been constructed and explored. The MLE estimations of the parameters were determined using R's adequacy model package. To calculate the bias of the model parameter and the root mean square error, a simulation study was done. The simulation study revealed that the proposed model is well-behaved. The findings also showed that the suggested model outperforms the current listed models on two real datasets when performance was compared.

ANOVA F Test of Non-Null Hypothesis

Guolong Zhao — 2024-02-16

ANOVA, a test of a null hypothesis, is limited in assessing the statistical significance of differences. This paper considers an ANOVA F test of the non-null hypothesis for comparing k group means. A margin is chosen for the difference of means between each group and the kth group. A non-null hypothesis is defined to be the difference equal to the margin instead of zero. Data are thus prepared under the non-null hypothesis. Then follows the derivation of the one-way ANOVA non-null F test and its power. It reduces to the classical F test on setting the margin equal to zero. The observed size of it is identical to that of the F test and is near the nominal level of significance. The observed power is close to the power in balanced designs. With the non-null F test, it enables inferences to extend to the equivalence of group means or the clinical significance of differences. An example is taken to analyze both non-inferiority trials and k-sample equivalence trials.

Estimation of Optimal Lock-Down and Vaccination Rate of a Stochastic SIR Model: A Mathematical Approach

Paramahansa Pramanik — 2024-01-25

This paper utilizes a stochastic Susceptible-Infected-recovered (SIR) model with a nonlinear incidence rate to estimate the optimal lock-down intensity and vaccination rate under the COVID-19 pandemic environment. We use a Feynman-type path integral control approach to determine a Fokker-Plank type equation of this system. Since we assume the availability of information on the COVID-19 pandemic is complete and perfect, we show the existence of a unique fixed point. A non-linear incidence rate is used because, it can be raised from saturation effects that if the proportion of infected agents is very high so that exposure to the pandemic is inevitable, then the transmission rate responds slower than linearity to the increase in the number of infections. The simulation study shows that with higher diffusion coefficients susceptible and recovery curves keep the downward trends while the infection curve becomes ergodic. Finally, we perform a data analysis using UK data at the beginning of 2021 and compare it with our theoretical results.

Improved Monitoring of Early-Warning Signs of an AMOC Collapse

Erhard Reschenhofer — 2024-01-25

This paper reviews a recent study predicting that the Atlantic Meridional Overturning Current circulation may collapse in the middle of this century and concludes that there are too many uncertainties to allow a reliable prediction. Even if the model used in that study is fairly adequate, its predictions depend heavily on the quality of the involved approximations, the choice of the circulation proxy, the method of trend estimation, the size of the rolling window used for the estimation of the second moments, the determination of the start time of ramping, etc. Forced to set lower targets, the focus is consequently shifted to the improved detection of early-warning signs like an increase in variance and autocorrelation. Two new estimation procedures are introduced. The first concerns the estimation of the trend and includes a new criterion for comparing the quality of different estimates. The second is a procedure for detecting changes in the first-order autocorrelation without any delay caused by an estimation window. The results obtained with these methods suggest that the autocorrelation increases erratically rather than steadily which would make forecasting based on extrapolation impossible.

Enhancing Multiple Frame Surveys: Improved Calibration and Efficient Bootstrap Techniques

Cherif Ahmat Tidiane Aidara — 2024-01-18

In recent years, multiple frame surveys have gained significant attention due to their applicability in capturing special or challenging-to-sample populations. This paper introduces two methodological advancements, the calibrated multiplicity estimator and without-replacement bootstrap techniques, in the field of multiple frame surveys. A comprehensive simulation study assesses their performance. The calibrated multiplicity estimator is demonstrated to outperform the multiplicity estimator, particularly in terms of mean squared error, with a ratio ranging from 0.6 to 0.8. Furthermore, the study shows that without-replacement bootstrap techniques perform favorably compared to their with-replacement counterparts. Future research directions include conducting more extensive simulations with real-world data and establishing the theoretical properties of the proposed estimator. This paper contributes to the growing body of knowledge on multiple frame surveys and their estimation methods.