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All Journal EIGEN MATHEMATICS JOURNAL Mikailalsys Journal of Mathematics and Statistics
Abdulkadir, Ahmed
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Engineering Mathematics Mechanical Engineering

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Novel Extended Weibull Regression Model for Investigating the Survival Times of Breast Cancer Patients Abdulkadir, Ahmed; Adubisi, Obinna Damian; Madaki, R. M.
Mikailalsys Journal of Mathematics and Statistics Vol 2 No 3 (2024): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v2i3.3840

Abstract

The new five-parameter alpha power generalized odd generalized exponentiated Weibull distribution is introduced, and some of its structural properties are derived. Its parameters are estimated by maximum likelihood, and a simulation study examines the accuracy of the estimates. A regression model is constructed based on the logarithm of the proposed distribution to investigate the survival times of breast cancer patients in Bauchi State, Nigeria. The applicability and flexibility of the novel model is proven by means of cancer dataset.
Crisping the Fuzzy ARIMA Intervals of Possibility for Short Term Forecasts Bakawu, Maigana Alhaji; Abdulkadir, Ahmed; Abbas, Umar Faruq; Baba, Ali Mohammed
Eigen Mathematics Journal Vol 8 No 1 (2025): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i1.272

Abstract

The Fuzzy autoregressive integrated moving average (FARIMA) model is a fuzzy-enhanced version of the autoregressive integrated moving average (ARIMA) model that yield improved prediction accuracy with fewer data observations as compared to the classical ARIMA models. The FARIMA time series utilizes membership functions of the fuzzy coefficients and generates forecasts in the form of possibility intervals. However, the FARIMA model does not provide crisp forecast values for forecasting future possibility intervals. This paper aims to simultaneously achieve in-sample and out-sample intervals of possibility forecasts by converting Fuzzy ARIMA possibility intervals into crisp values. The method is tested on exchange rate of the New Taiwan Dollar (NTD) against the United States Dollar (USD) and the annual average mean surface air temperature of Nigeria. The results demonstrate that the proposed method produces out-of-sample possibility interval forecasts that closely align with those obtained using observed values in most cases. In addition, forecasts performance evaluation results indicate that the proposed method produces smaller MAPE and RMSE values in LB predictions while approximately competing in UB predictions compared to the considered methods in the literature. Moreover, the proposed method has advantage of forecasting future possibility intervals without relying on crisp out-of-sample observed values. This implies the method could aid policy makers in determining the worst and best projected bounds that could be used for making future decisions without actual out-of-sample crisp observations.
On the Comparison of PAR, DARMA, and INAR in Modeling Count Time Series Data Buba, Haruna; Abdulkadir, Ahmed; Lasisi, Kazeem E.; Bishir, A.; Mashat, Strong Yusuf
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6312

Abstract

This study evaluates the forecasting and fitting performance of three advanced models—Poisson Autoregressive (PAR), Discrete Autoregressive Moving Average (DARMA), and Integer-Valued Autoregressive (INAR) for count time series data exhibiting complex features such as autocorrelation, overdispersion, and zero inflation. Both simulated and empirical datasets were analyzed, and model performance was assessed using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). The results indicate that PAR models significantly outperform DARMA and INAR models, achieving substantially lower AIC (482.53 vs. >5,310,479) and RMSE (3,742 vs. 246,682), highlighting their robustness in handling periodic trends and autocorrelation. In contrast, standard Poisson regression performs poorly under overdispersion, with an AIC approaching 5.3 million, while zero-inflated datasets compromise error metrics such as MAPE due to division by zero. Although DARMA and INAR models perform comparably, they are less effective in capturing extreme fluctuations or sudden spikes. These findings emphasize the limitations of conventional models and point to the need for more flexible approaches, such as hybrid ZIP-INAR models or Bayesian methods, to effectively manage overdispersion and zero inflation. The study concludes with a practical recommendation to prioritize PAR models when modeling autocorrelated count data.
Co-Authors Abbas, Umar Faruq Adubisi, Obinna Damian Baba, Ali Mohammed Bakawu, Maigana Alhaji Bishir, A. Buba, Haruna Lasisi, Kazeem E. Madaki, R. M. Mashat, Strong Yusuf