Applied in modeling asset returns, revenue growth and margin assumptions around a base case, and inflation or rate paths in valuation and credit models.

Applied in turning low, base and high cases into a range, estimating construction cost and schedule, and forecasting sales with limited data.

Applied in modeling bounded rates such as occupancy, utilisation, recovery rates and probabilities of success, between a set minimum and maximum.

Applied in project cost and schedule estimates from expert input, three-point capex and opex assumptions, and risk analysis in project finance and development models.

Applied in modeling positive, right-skewed amounts such as claim sizes and loss severities, the timing of market events, and service times in operations.

Applied when every value in a range is equally likely, such as an exit multiple or timing assumption with no clear base case, and in random sampling.

Applied in modeling stock prices, asset values and commodity prices that can't fall below zero, and right-skewed variables such as income or project costs.

Applied in modeling equipment lifespans and failure rates in infrastructure and energy assets, wind speeds in renewables models, and time to default in credit risk.

Applied in modeling maximum losses and worst-case market moves, peak demand or prices, and the largest events in a stress test.

Applied in modeling minimum levels such as the lowest sales or weakest cash flow period, minimum performance thresholds, and downside floors in financial plans.

Applied in modeling market penetration and new product adoption, growth that levels off over time, and variables with heavier tails than the normal.

Applied in modeling fat-tailed portfolio and market returns, estimating means from small samples, and stress-testing beyond what a normal distribution allows.

Applied in modeling the time between events such as defaults, outages or customer arrivals, time to default in credit risk, and service times in operations.

Applied in modeling customer or revenue concentration, where a few items drive most of the total, and the risk of very large losses or claims.

Applied in modeling the number of defaults in a loan pool, the number of deals or contracts won, and pass or fail counts across repeated trials.

Applied in modeling how many events happen in a period, such as defaults, claims, outages or transactions, including rare events.

Applied in sampling a finite pool without replacement, such as testing loans or invoices in a portfolio review, defect sampling and audit sampling.

Applied in modeling how many attempts it takes to reach a target, such as pitches to win a set number of mandates, and claim or default counts that vary more than a Poisson.

Applied in modeling the number of attempts until the first success, such as the first deal closed, the first customer purchase or the first default.

Applied when each of a set of discrete outcomes is equally likely, such as the exit year, the number of units sold or the test group a customer is assigned to.

Applied in modeling events that either happen or not, such as a contract renewal, a permit approval, a refinancing or a customer purchase.