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Research Article
Weibull Distribution and Approximation, by the Finite Volume Method, of the Ultim Ruin Probability Constructed from the Hawkes Variable Memory Process
Souleymane Badini*
,
Frédéric Bere
Issue:
Volume 14, Issue 4, August 2025
Pages:
118-125
Received:
31 May 2025
Accepted:
16 June 2025
Published:
4 July 2025
Abstract: It measures the risk that a system or company fails to maintain its elf over time. In this article, we provide an approximation of the probability of ruin at the infinite horizon whose inter-arrivals of claims follow the Hawks process and the amount of claims follows the Weibull distribution, with independence between these two processes. Using the Finite Volume Method is a numerical approach for solving partial differential equations. It consists of dividing the computational domain into discrete volumes and applying local approximations to obtain a global solution. This method can be used to estimate complex probabilities., a stochastic model with variable memory, it is possible to capture the temporal dependence of events. This allows us to analyze situations where the past directly influences the probability of occurrence of future events. This approximation is done using the finite volume method, which is a numerical approach for solving partial differential equations. It consists of dividing the computational domain into discrete volumes and applying local approximations to obtain a global solution. This method can be used to estimate complex probabilities. This is the case in our work; which consists of solving a second-order integro-differential equation, two cases of which are considered on the Weibull parameter η: if η=1, then the distribution of claim amounts is exponential. On the other hand, if η≥2, then the results lead us to a system of linear equations for which we use the finite volume method to obtain a numerical solution.
Abstract: It measures the risk that a system or company fails to maintain its elf over time. In this article, we provide an approximation of the probability of ruin at the infinite horizon whose inter-arrivals of claims follow the Hawks process and the amount of claims follows the Weibull distribution, with independence between these two processes. Using the...
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Research Article
Robust D-optimal Designs for the First-degree and the Second-degree Kronecker Model for Mixture Experiments
Mike Cherutich*,
Jopseph Arap Koske,
Mathew Kosgey
Issue:
Volume 14, Issue 4, August 2025
Pages:
126-137
Received:
24 May 2025
Accepted:
6 June 2025
Published:
14 July 2025
Abstract: Many practical problems are associated with the investigation of mixture of m ingredients, which are assumed to influence the response through the proportions in which they are blended together. Such problems lend their applicability to mixture experiments. Mixture experiments can be modeled using Scheffe’ or Kronecker models. For the first-, second-, and third-degree Kronecker models, D-optimal designs for the mixture experiments have been derived by various authors. This creates uncertainties to an experimenter, hence the need for robust designs. The objective of this study is to derive robust D-optimal designs for mixture experiments in the first- and the second-degree Kronecker model for mixture experiments. In order to achieve this, the D-optimal weights for the designs in the first-degree and those of the second degree Kronecker models are obtained. The model robust D-Optimality criterion is then used. The D-Optimal designs are obtained by maximizing this criterion which involves differentiating, equating to zero and solving for , r1 and r2 in order to obtain the optimal values. In conclusion the results of this study demonstrate the existence of model robust D-optimal Kronecker model mixture experiments for the first- and the second-degree Kronecker models.
Abstract: Many practical problems are associated with the investigation of mixture of m ingredients, which are assumed to influence the response through the proportions in which they are blended together. Such problems lend their applicability to mixture experiments. Mixture experiments can be modeled using Scheffe’ or Kronecker models. For the first-, secon...
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Research Article
Statistical Analysis on Consequences of Rising Fuel Prices on Citizens
Issue:
Volume 14, Issue 4, August 2025
Pages:
138-154
Received:
15 June 2025
Accepted:
27 June 2025
Published:
4 August 2025
Abstract: This study investigates the broad economic, behavioral, and psychological impacts of rising fuel prices on urban residents in Vadodara, India. Primary data was collected from two key areas Fatehgunj and Tarsali using structured questionnaires to capture citizens’ responses to the ongoing increase in fuel costs. The study had multiple objectives: to evaluate the direct consequences of rising fuel prices on household expenditure, assess the readiness of people to adopt alternative transportation methods, analyze fuel spending across different age groups and income levels, and understand how individuals are adjusting to manage this financial pressure. Furthermore, the study explores the impact of fuel inflation on mental health and seeks citizens’ suggestions on how this issue might be addressed. An additional comparative objective was introduced to examine whether similar fuel pricing challenges are experienced in another developing country, specifically Kenya. A range of statistical tools were employed for data processing and analysis, including SPSS, R, Python, Microsoft Excel, and Power BI. These tools were used to conduct descriptive and inferential analysis, create data visualizations, and draw correlations between demographic variables and spending behaviors. The results reveal a significant shift in travel habits, increased financial stress among middle- and lower-income households, and growing public concern about long-term affordability. Many respondents reported cutting back on non-essential expenses, while others expressed willingness to switch to fuel-efficient vehicles or public transportation. These findings provide valuable insights for policymakers, economists, and urban planners aiming to develop effective strategies to ease the burden of rising fuel prices on the general public.
Abstract: This study investigates the broad economic, behavioral, and psychological impacts of rising fuel prices on urban residents in Vadodara, India. Primary data was collected from two key areas Fatehgunj and Tarsali using structured questionnaires to capture citizens’ responses to the ongoing increase in fuel costs. The study had multiple objectives: to...
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Research Article
Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics
Bhushan Poojary*
Issue:
Volume 14, Issue 4, August 2025
Pages:
155-159
Received:
14 July 2025
Accepted:
24 July 2025
Published:
11 August 2025
Abstract: We propose a novel theoretical framework in which energy is generalized to a bicomplex quantity, significantly extending previous formalisms that treated energy as a complex number. In this bicomplex approach, energy comprises two distinct imaginary components arranged orthogonally, providing a richer algebraic structure. By carefully defining arithmetic operations within this bicomplex space, we demonstrate that division naturally introduces a geometric scaling factor identified explicitly as the fine-structure constant α. The emergence of α within this algebraic structure provides new insights into its fundamental geometric interpretation and underscores its role as a universal scaling factor connecting quantum-scale interactions to larger-scale phenomena. We present rigorous algebraic derivations and systematically define the arithmetic rules governing bicomplex quantities. Additionally, we clarify how these algebraic properties facilitate novel connections across various domains, including quantum mechanics, holographic theories, and theoretical physics frameworks aimed at unification. Specifically, the introduction of bicomplex energy allows us to interpret quantum mechanical processes and holographic projections in a unified mathematical context, offering fresh perspectives on longstanding theoretical challenges. The proposed framework not only deepens theoretical understanding but also generates experimentally testable predictions. These include unique signatures that could manifest in high-precision quantum electrodynamics experiments, as well as potential observable effects in advanced holographic or quantum-gravity-inspired setups. The framework invites further exploration into how higher-dimensional algebraic structures might underlie physical constants and fundamental interactions, providing a robust mathematical foundation for future theoretical and experimental investigations.
Abstract: We propose a novel theoretical framework in which energy is generalized to a bicomplex quantity, significantly extending previous formalisms that treated energy as a complex number. In this bicomplex approach, energy comprises two distinct imaginary components arranged orthogonally, providing a richer algebraic structure. By carefully defining arit...
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Research Article
Modelling the Relationship Between Trade Openness, Macroeconomic Variables and Economic Growth in Ghana Using Ardl Models
Ebenezer Ayaaba*,
Anuwoje Ida L. Abonongo
Issue:
Volume 14, Issue 4, August 2025
Pages:
160-177
Received:
4 July 2025
Accepted:
21 July 2025
Published:
15 August 2025
Abstract: This study looked at the interconnections among trade openness, national income (GDP), investment, exchange rate, government spending, financial development and inflation in Ghana employing the autoregressive distributed lag (ARDL) model. The bounds cointegration, as applicable within the ARDL modelling was carried out to check the existence or otherwise of long run relationships among the economic variables while the error correction model (ECM) was also used to capture the short-term relationships among the variables. Unlike known previous studies in Ghana, this study made use of three trade openness proxies including ratio of imports plus exports to GDP (OPEN1), ratio of export to GDP (OPEN2) and the ratio of import to GDP (OPEN3). With GDP growth as endogenous variable, the bound co-integration analysis results showed that there exists co-integration among GDP, openness to trade and the macroeconomic variables included in the study. In this study, the short-run results found that openness to trade and government spending had significant positive effects on Ghana’s GDP growth. However, investment, exchange rate and financial development were found to be impacting growth in GDP significantly but negatively. In the long term, trade openness and government spending again had positive influence on GDP growth whiles investment, real effective exchange rate and financial development still impacted GDP growth significantly and negatively at 5 percent significance level. This study recommends among others things that the government of Ghana should reduce trade barriers and streamline regulations in critical sectors to promote GDP growth in Ghana.
Abstract: This study looked at the interconnections among trade openness, national income (GDP), investment, exchange rate, government spending, financial development and inflation in Ghana employing the autoregressive distributed lag (ARDL) model. The bounds cointegration, as applicable within the ARDL modelling was carried out to check the existence or oth...
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Research Article
A Study of Public Safety in Vadodara
Sheila Cherono*,
Frasiah Wambui Kariuki
Issue:
Volume 14, Issue 4, August 2025
Pages:
178-202
Received:
12 June 2025
Accepted:
27 June 2025
Published:
18 August 2025
Abstract: This study aims to evaluate public safety perceptions and street crime patterns in Vadodara, a major city in Gujarat, India. Data was collected from both primary and secondary sources to provide a comprehensive understanding of safety concerns across the city’s four zones: North, East, West, and South. The primary data was obtained through field surveys conducted within these zones, capturing citizen perceptions and experiences related to safety. Secondary data was sourced from the Office of the Commissioner of Police, Vadodara, which provided official records of street crimes over the past four years, categorized zone-wise. The study employed various statistical tools, including Microsoft Excel for data management and visualization, R programming for advanced statistical analysis, and SPSS software for in-depth data interpretation. Findings from the analysis reveal a significant variation in perceived safety between day and night, with the majority of residents reporting a greater sense of security during daylight hours. Furthermore, certain zones displayed higher incidences of street crimes such as theft, chain snatching, and assault, indicating spatial disparities in crime concentration. The study highlights the importance of targeted policing strategies and enhanced night-time surveillance in high-risk areas. These insights can assist local authorities in formulating evidence-based policies to improve urban safety and strengthen community trust in law enforcement.
Abstract: This study aims to evaluate public safety perceptions and street crime patterns in Vadodara, a major city in Gujarat, India. Data was collected from both primary and secondary sources to provide a comprehensive understanding of safety concerns across the city’s four zones: North, East, West, and South. The primary data was obtained through field su...
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