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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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