European Journal of Mathematics and Statistics

Gauss Metric on the Kummer Surface

Masahito Hayashi — 2025-02-17

On the Kummer surface, we have obtained two different Gauss metrices by parametrizing it in two ways. We have found that these Gauss metrices are not Ricci flat. The double sphere, which is the special case of the Kummer surface, has the Kähler metric and the first Chern class of it does not vanish. Its metric is the Einstein metric which is not Ricci flat.

Inverting Symmetric Positive Definite Matrices using Divide and Conquer Mathematical Technique with LU Factorization

Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman — 2025-02-24

We looked at the solution of a system of equations Ax=b with symmetric positive definite coefficient matrix A that has singular and nearly singular values. Our technique, which is based on the Divide and Conquer strategy, combines the LU Factorization algorithm with the Divide-and-Conquer technique (D&C algorithm). The matrix was transformed into a product of the type LU using the LU Factorization, where L is a lower triangular matrix and U is an upper triangular matrix. MATLAB was used to implement the algorithm and simulate it as a user-subroutine. In order to reduce the round-off error, particularly for sensitive systems, the user-subroutine takes into account MATLAB characteristics. A non-singular matrix and an ill-conditioned matrix were both numerically demonstrated. Analysis was done on the impact of round-off error. We contrasted the results with those from earlier studies that employed LU factorization.

The Arcsine Log-Logistic Distribution and Its Applications

Md. Aftab Moral — 2025-03-15

This article introduces Arcsine Log-logistic (AL-L) distribution which is a member of Arcsine-G family proposed by Rahman. The different properties of AL-L distribution have been discussed. The distribution of various order statistics are obtained. Maximum Likelihood Estimation (MLE) technique is used to estimate the model parameters. Finally, for testing the practicability of proposed model we have been used two different datasets.

Time Series Modeling of National Hospital Insurance Fund Coverage in Kenya

Hellen Wawira Ndwiga — 2024-12-30

National Hospital Insurance Fund (NHIF) is a state-owned organization that was established in 1966 with the goal of providing Kenyans with social health insurance that is easily accessible, affordable, long-lasting, and of high quality. Only 24% of Kenyans have access to NHIF, this may affect the implementation and outcome of Universal Health Coverage (UHC). NHIF mandate can only be achieved if the whole population is under an insurance health cover. Understanding patterns, trends and forecasting of NHIF population Coverage using time series analysis would help in policy formulation and planning for proper implementation of UHC in Kenya. The main objective of the study was to model and forecast Kenya’s NHIF population coverage using Seasonal Autoregressive Integrated Moving Average model. Time series research design was used as it involved data that was measured at regular intervals over a significant number of observations. This design followed the Box-Jenkins Seasonal Autoregressive Integrated Moving Average (SARIMA) model. Simulated time series data on NHIF enrollment for the period 1998–2023 was used for this study. R and R-studio was used in the statistical analysis of the data. The model which exhibited the least Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values was picked by fitting the SARIMA model. Finally, forecasting of the data after following the three Box-Jenkins methodologies, that is, model identification, estimation of parameters and diagnostic check is done. Having an AIC value of 2265.00 and BIC value of 2279.66 SARIMA (1,1,3) (0,1,1)4 model fitted the data well. This modelpassed residual normality test and the forecasting evaluation statistics shows the errors as RMSE = -1263.392, MAPE = 5.872978 and MAE = 11197.31 The 3-year ahead forecasts showed that the enrollment had overall increasing trend. However, moving further into the future forecast the confidence intervals tend to widen. This indicated that the model’s predictions became less certain with time. The SARIMA model proved to be a suitable approach for capturing the underlying patterns in the NHIF enrollment data, providing reasonable forecasts. The findings of the study would lead to robust sensitization by both national and county government and all other stakeholders on the importance of National Hospital Insurance Fund coverage which would lead to increased enrollment from 24% to almost 100% through the Social Health Authority (SHA). This in turn would lead to attainment of the Universal Health Coverage an objective of the third Sustainable Development Goal that stipulates healthy lives and promotes well-being for all at all ages.

A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture

Masahito Hayashi — 2024-11-13

For quadratic curves over finite fileds, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a quadratic curve analogue of the modular form in the Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian sum and also possesses some modular transformation structure.