Asian Journal of Probability and Statistics

An Ishita-G Family of Continuous Probability Distributions: Theory, Properties, Simulation and Application

Nasiru Yakubu, Adamu Abubakar, Bello A. Rasheed, A. U. Shelleng — Mon, 31 Aug 2026 00:00:00 +0000

This study introduces a new family of continuous probability distributions, termed the Ishita-G family, using the Transformed-Transformer (T-X) method. The Ishita-G family is generated by combining the Ishita distribution with a baseline distribution through a generator approach, thereby producing more flexible models with varied density and hazard-rate shapes. Three special submodels of the family are defined: the Ishita-Exponential, Ishita-Weibull, and Ishita-Pareto distributions. The study investigates important statistical properties of the Ishita-Exponential distribution (IshExD), including the probability density function, cumulative distribution function, survival function, hazard-rate function, and moment-generating function. The validity of the proposed density function is also established mathematically. The parameters of the IshExD are estimated using maximum likelihood estimation, and a Monte Carlo simulation study is conducted to examine the consistency and efficiency of the estimators. The simulation results show that the estimators perform well as the sample size increases, with decreasing biases and mean squared errors. Furthermore, the usefulness of the proposed family, through the IshExD, is demonstrated using a real-life dataset comprising failure times for repairable items. Model-comparison measures, including the Akaike information criterion (AIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC), and Kolmogorov-Smirnov statistic, show that the Ishita-Exponential distribution outperforms the competing models considered. The results indicate that the Ishita-G family is a flexible and useful contribution to the literature on generalised probability distributions.

Alternative Methods For Solving Some Random Walk Problems: First Passage Times

Felgona Tana Omondi, Fredrick Onyango, Isaac Owino — Wed, 19 Aug 2026 00:00:00 +0000

This study examines alternative methods for solving selected first-passage-time problems in one-dimensional random walks. A simple random walk is considered in which movement to the right occurs with probability p and movement to the left with probability q=1p. The study focuses on first-passage-time probabilities, expected values, variances, and the jth passage time. Its central approach is a proposed counting formula linked to Catalan numbers and related combinatorial identities. The counting structure is used to represent the probability of reaching x=1 for the first time after an odd number of steps and to obtain a Catalan-number form for the first passage-time distribution. The manuscript further derives the expected value and variance of the first passage time using two approaches,! including! generating-function arguments and the proposed counting method. In addition, counted coefficients for successive passage times are examined and used to formulate a general expression for the jth passage time through a Catalan-Ballot convolution identity. The results illustrate a combinatorial connection between first-passage-time probabilities and Catalan-number structures while providing an alternative route to quantities that have also been approached by difference equations, conditioning, generating functions, and related probabilistic methods. The analysis is restricted to one-dimensional random walks, and the direct applicability of the proposed counting formula to higherdimensional walks is not established.

Dynamics of Social-Media-Driven Consumerism and Environmental Accumulation: A Review and Mathematical Analysis

Syed Azhara Yaqoob, Gowhar Hussain Bhat — Mon, 24 Aug 2026 00:00:00 +0000

Background: Consumerism has become a defining feature of modern economies, significantly amplified by the expanding reach of social media platforms. Through viral content, influencer marketing, and algorithmic recommendations, consumer demand spreads rapidly among individuals and communities, accelerating market saturation while generating substantial environmental externalities. The production and disposal of consumer goods contribute significantly to greenhouse gas emissions, resource depletion, and waste generation, creating an urgent need to understand the coupled dynamics of social-media-driven consumerism and environmental accumulation.

Purpose: This paper aims to synthesize existing literature from marketing science, social network theory, mathematical epidemiology, and environmental economics to establish a unified framework for understanding the interconnected processes of social-media-driven consumerism and environmental externalities. Specifically, we develop a mathematical model that captures the feedback loops linking consumer demand, social media intensity, consumption behaviour, and environmental accumulation, hereby enabling the identification of key parameters driving system behaviour and the derivation of policy recommendations for sustainable consumption.

Methods: We develop a system of coupled nonlinear ordinary differential equations modelling the interaction among four key variables: consumer demand D(t), social media intensity S(t), consumption C(t), and environmental externality E(t). The model extends the classic Bass diffusion model to include dynamic social media influence and couples it with content generation dynamics and environmental accumulation. We perform a comprehensive sensitivity analysis by systematically varying key parameters (q, \(\mu\), \(\delta\), \(\omega\)) while holding others at baseline values. A heatmap of market saturation times and a phase diagram of dynamical regimes are constructed to identify critical thresholds and nonlinear responses.

Results: The analysis reveals explosive growth phases with rapid market saturation occurring within 8-10 days under baseline parameters, after which demand and consumption stabilise at D ≈ 98.93 and C ≈ 128.47. Environmental externalities accumulate slowly and persistently with a time constant T_E= 50 days, approaching steady-state E^*= 642.35 – nearly six times the baseline consumption level. The imitation coefficient q and content generation rate \(\mu\) are identified as critical accelerants for market saturation, while the environmental mitigation rate \(\omega\) is the most important parameter for controlling long-term environmental damage. Four distinct dynamical regimes are identified: Dormant ((p + q)/\(\delta\) ¡ 1), Slow Takeoff (1 ¡ (p + q)/\(\delta\) ¡ 2), Viral Explosion (2 ¡ (p + q)/\(\delta\) ¡ 5), and Hyper-viral ((p + q)/\(\delta\) ¿ 5), with baseline parameters (p + q)/\(\delta\) = 8.4 placing the system firmly in the hyper-viral regime.

Conclusions: Social-media-driven consumerism exhibits hyper-viral dynamics that rapidly saturate markets and generate persistent environmental externalities. The positive feedback loop D→C→S→D drives explosive growth, and breaking any single link requires unrealistic parameter changes. Environmental mitigation investments (increasing \(\omega\)) are identified as the most effective policy intervention, reducing steady-state environmental damage by 50% when doubled. Content moderation policies (reducing \(\mu\)) may be more effective than influencer regulation (reducing q) in slowing consumerism. The rapid market saturation and persistent environmental accumulation highlight the urgency of intervention, as the dangerous lag between consumption and observable environmental damage requires immediate action to avoid irreversible consequences.

Note: The model is presented as an illustrative deterministic framework that has not yet been empirically calibrated; therefore, the numerical results should be interpreted qualitatively to identify system dynamics and key leverage points rather than as precise quantitative predictions.

Integrated Response Surface Methodology with Gradient Boosting in Modelling Potato Post-Harvest Losses

Erick Kirui — Tue, 01 Sep 2026 00:00:00 +0000

Post-harvest losses remain a persistent constraint to potato value chains, particularly where cold-chain systems and storage facilities are limited. This study presents a simulation-based demonstration of an integrated hybrid modelling framework that combines Response Surface Methodology (RSM) with Gradient Boosting Machines (GBM) to model potato post-harvest deterioration under different storage conditions. The objective was to assess the methodological feasibility of combining an interpretable polynomial response surface with a machine-learning residual-correction model. A Central Composite Design was developed using six storage-related variables: temperature, relative humidity, storage duration, light exposure, mechanical damage and curing duration. Synthetic observations were generated through Monte Carlo simulation using post-harvest biological parameter assumptions from the literature. Weight loss, sprouting index and rotting loss were standardised and combined through Principal Component Analysis to develop a Composite Loss Index (CLI). A second-order RSM model was first fitted to the CLI to estimate linear, quadratic and interaction effects among the predictors. The unexplained residual variation from the RSM model was then modelled using GBM to capture higher-order nonlinearities and complex interactions not represented by the polynomial surface. In the simulated environment, the hybrid RSM-GBM model achieved better predictive performance than the standalone RSM and GBM models. Storage duration, relative humidity, temperature and variety were the dominant contributors to simulated post-harvest deterioration patterns. The findings indicate that combining interpretable response surface modelling with non-parametric residual learning can improve prediction while retaining useful explanatory structure. However, all results are based on simulated data and should therefore be interpreted as preliminary computational evidence rather than empirical agricultural findings. Further validation using controlled and field-based potato storage observations is required before practical application.