Probabilistic Modelling for Business Data
Fitting continuous distributions and zero-inflated count models to interpret uncertainty, tails, and rare/repeated events in business data.
Type
Methodological academic work
Area
Probabilistic Modelling · Business Analytics
Tools
R · fitdistrplus · glmmTMB · DHARMa · VGAM
Techniques
MLE · Goodness-of-fit · AIC / BIC · Lognormal · Gamma · Zero-inflated models
Output
Probabilistic model comparison
Value
Academic work where I compared distributions and probabilistic models using R, maximum likelihood, and fit criteria to interpret uncertainty and business-data structure.
Observations in continuous fit
Selected Lognormal AIC
Selected ZINB AIC
01 / Fast scan
Case in 60 seconds
A quick scan of the case: what was happening, what needed to be solved, what I did, and what value is demonstrated.
Situation
SBusiness data often includes skewed monetary variables, low-frequency events, many zeros, or concentrated counts. Modelling them properly avoids defaulting to normality and helps interpret uncertainty, risk, and operational variability.
Task
TAcademic work where I compared distributions and probabilistic models using R, maximum likelihood, and fit criteria to interpret uncertainty and business-data structure.
Action
A- 01Explore empirical data shape.
- 02Propose candidate distribution families.
- 03Estimate parameters by maximum likelihood.
- 04Compare visual fit and AIC/BIC criteria.
Result
R- For positive, skewed monetary variables, the Lognormal can clearly outperform the Normal.
- In count data with variance far above the mean, Poisson can be insufficient.
- Excess zeros require distinguishing structural zeros from sampling zeros.
- Transferable to prices, costs, revenue, purchase frequency, incidents, leads per account, or risk events.
- Useful for analysts who need to quantify uncertainty and avoid simplistic distribution assumptions.
- 309 · Observations in continuous fit
02 / Context
Problem
This section explains the business or analytical challenge before going into technical detail.
02.1
Executive summary
Methodological case showing the ability to choose distributions according to data shape, compare models with objective criteria, and validate whether a model captures tails, overdispersion, or excess zeros.
02.2
My role
Individual academic works. I fitted models in R, compared alternatives using AIC/BIC and goodness-of-fit tests, and validated simulated residuals in count models.
03 / Method
Approach
Methods, tools, and workflow. This shows how I structured the analysis.
03.1
Data & methods
- Fitting continuous distributions to a positive, skewed monetary variable.
- Comparison of Normal, Lognormal, Gamma, and Weibull with fitdistrplus.
- Poisson, Negative Binomial, ZIP, and ZINB count models with glmmTMB.
- Diagnostics for overdispersion, zero inflation, and simulated residuals with DHARMa.
03.2
Process
- 01Explore empirical data shape.
- 02Propose candidate distribution families.
- 03Estimate parameters by maximum likelihood.
- 04Compare visual fit and AIC/BIC criteria.
- 05Validate diagnostics of the selected model.
- 06Translate results into business interpretation.
04 / Decision
Evidence and impact
Outputs, findings, and implications translated into decisions or professional value.
04.1
Key findings
- For positive, skewed monetary variables, the Lognormal can clearly outperform the Normal.
- In count data with variance far above the mean, Poisson can be insufficient.
- Excess zeros require distinguishing structural zeros from sampling zeros.
- AIC/BIC and residual diagnostics help avoid selecting models only by intuition.
04.2
Business implications
- Transferable to prices, costs, revenue, purchase frequency, incidents, leads per account, or risk events.
- Useful for analysts who need to quantify uncertainty and avoid simplistic distribution assumptions.
05 / Close
Professional close
Limitations, next steps, and available assets. This keeps the case honest and actionable.
05.1
Limitations
- Academic and methodological cases.
- One count dataset is not suitable as a highlighted public case due to its sensitive topic; it should be communicated generically if mentioned.
- Does not include full multivariate predictive models.
05.2
What I would do next
- Apply to real business datasets with explanatory variables.
- Compare with Bayesian or machine-learning models depending on the case.
- Create scenario simulators for operational decisions.
05.3
Assets
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