"Understanding Discrete Statistical Distributions: A Medical Research Perspective"

Abstract

Background: Statistical distributions play a critical role in medical sciences by providing the mathematical foundation for analysing and interpreting biomedical data. From clinical trials to epidemiological research, their
appropriate application enables informed decision-making, trend identification, and evaluation of treatment efficacy. Distributions such as Normal (via the Central Limit Theorem), Binomial, Poisson, Exponential, and Weibull are widely used for modelling continuous data, binary outcomes, rare events, and time-to-event data, respectively.
Aims/Objectives: To explore the theoretical framework and practical utility of key statistical distributions—particularly discrete distributions— in medical research, and to demonstrate their applications using real- world numerical examples.

Methods: A descriptive analytical approach was adopted, integrating theoretical concepts with mathematical formulations. Applications were illustrated through examples from clinical trials, diagnostic testing, epidemiology, and survival analysis.
Results: Quantitative analysis demonstrated the effectiveness of discrete distributions in medical contexts. The Binomial model showed probabilities of 0.2508 (25.08%) for treatment success and 0.323 (32.3%) for diagnostic accuracy. The Poisson distribution yielded probabilities of 0.036 (3.6%) for rare disease incidence and 0.090 (9.0%) for patient arrivals. The Geometric distribution indicated probabilities of 0.0656 (6.56%) for relapse timing, with an expected response time of 3.33 weeks. The hypergeometric distribution produced probabilities of 0.256 (25.6%) in finite population sampling scenarios. The Negative Binomial distribution demonstrated a 0.055 (5.5%) probability of repeated relapses, effectively capturing over dispersion in medical data.
Conclusion: Statistical distributions are essential in medical research, enabling accurate modelling, reliable inference, and evidence-based clinical decision-making.

How to cite this article:
Chintada G S, Rao K S, Mishra S K, Jena S K, Title: “Understanding Discrete Statistical Distributions: A Medical Research Perspective” . IAP J. Med. Educ. Res. 2025;2(2):19-25.