IDOWU ADENIRAN GBOLAHAN

Mathematics

At the Mathematics department office

Appointment on Visitation important

Topic: A Framework For Fraud Detection Using The Pareto-Inverse-Logistic Distribution: Derivation, Properties, And Implementation

Description:

Introduction

The inverse-logistic distribution, derived from the standard logistic distribution, exhibits a unique self-inverse property and heavy-tailed behavior, making it valuable for modeling positive-valued phenomena across economics, survival analysis, hydrology, and network science. Despite its theoretical appeal and broad applicability, its potential—particularly when extended through the T-X family—remains underexplored in critical domains such as fraud detection, where extreme events dominate losses.

 Aims and Objectives

This research aims to provide a comprehensive treatment of the inverse-logistic distribution, deriving it from first principles and analyzing its key mathematical properties. It seeks to extend the distribution via the T-X family to formulate a novel Pareto-inverse-logistic distribution. The primary objective is to demonstrate the practical utility of this new model by developing a robust anomaly scoring and dynamic thresholding framework for fraud detection, with comparative performance evaluation against existing methods.

 Methodology

The study employs a dual approach: theoretical derivation using transformation techniques and the T-X family framework to construct the Pareto-inverse-logistic distribution, establishing its closed-form CDF, PDF, and hazard function; and applied development, wherein the model is operationalized for fraud detection through anomaly scoring, dynamic threshold selection, and implementation within a hybrid framework combining extreme value theory with machine learning. Performance is evaluated using detection rates, false positive rates, and AUC metrics in a banking case study.

 Expected Results

The Pareto-inverse-logistic distribution is expected to exhibit superior tail performance compared to standard Pareto models. In fraud detection, it is anticipated to achieve higher detection rates for large-scale fraudulent transactions while maintaining a low false positive rate, resulting in a measurable reduction in fraud-related losses.

 Contribution to Knowledge and Society

This research contributes theoretically by introducing a new tractable distribution to the T-X family with closed-form expressions. Its societal contribution lies in providing a statistically principled, interpretable tool for fraud detection that complements machine learning approaches, enabling organizations to better identify extreme anomalous events and substantially mitigate financial losses.

#	Certificate	School	Year
1.	Ph.D (Statistics)	Mathematics, University of Lagos, Akoka	2019

A Computational Framework for Convolution of Transformed-Transformer Distributions

Introduction

The Transformed-Transformer (T-X) family enables flexible statistical modeling across actuarial science, reliability engineering, and survival analysis. While these distributions capture skewness, heavy tails, and nonstandard hazard behavior effectively, their utility for aggregate modeling—where sums of random variables are required—remains limited because convolution operations are analytically intractable due to their complex composite structure.

Aim and Objectives

This study develops a computational framework for evaluating convolutions of T-X distributions. Objectives include: (1) formulating a general pdf-based convolution framework; (2) implementing Bayesian Quadrature (BQ) as the principal method, with Warped Bayesian Quadrature and Flexible Quasi-Monte Carlo as comparisons; (3) validating through Gamma-Pareto, Gamma-X, and Weibull-Pareto benchmarks; and (4) developing surrogate formulas for numerically computed convolutions.

 Methodology

The approach transforms convolution integrals to the unit interval [0,1] and applies BQ, which models integrands as Gaussian processes to exploit smoothness and quantify numerical uncertainty. Implementation in Python uses benchmark problems with exact solutions for validation.

 Expected Results and Contributions

BQ is expected to achieve superior accuracy under equivalent computational budgets. Contributions include: a unified theoretical formulation bridging flexible distribution construction with aggregate modeling; a structured computational methodology tailored to T-X convolution; and practical tools enabling accurate aggregate analysis for actuarial risk assessment, reliability engineering, and complex system modeling.

IDOWU GBOLAHAN is a Senior Lecturer at the Department of Mathematics

IDOWU has a Ph.D in Statistics from Mathematics, University of Lagos, Akoka